In the long shadows of early dusk, a large black Mercedes with blacked-out windows picked me up from my hotel and whisked me through Gaza City's dusty, sullied streets. The roads, strewn with rubbish, were largely empty: Gaza was preparing for an Israeli incursion and the routine was familiar.

Last month I was invited to attend iftar - the evening meal during Ramadan - with a senior Hamas leader in Gaza. I can't name him because I was invited only on condition of anonymity. His wife had prepared a feast at his home in southern Gaza, but following an Islamic Jihad strike on an Israeli military base earlier that week he had chosen to stay in Gaza City, where the new Hamas government is headquartered. There were reports that the Israeli army was planning a large incursion and intended to cut the strip in two, separating Rafah and the south from Gaza City and the north. This meant I had the opportunity to have dinner with Hamas, and witness an internal debate within the senior leadership that is rarely seen by outsiders, particularly those from the west.

Since its takeover of the Gaza strip in June after fierce fighting with Fatah, Hamas, which had been elected largely because of its militancy against Israel, had quietened its guns but was still taking the heat for any violence coming out of Gaza. A few days earlier in his office, the Hamas leader had heard a Fatah official in Ramallah on television goad Hamas for not sticking to its resistance mandate. Since Hamas' election victory in 2006, hostilities between the two Palestinian factions have worsened, culminating in the bloody "battle of Gaza" in June this year, in which more than 100 people were killed. "We want to keep our heads down," the leader had told me, "and try to get Gaza running properly. We don't need to give the Israelis more reasons to kill us."

There were reports of Israeli tanks massing at the northern and southern ends of the strip and the leader had called "his friend", an Israeli journalist in Israel. The exchange in Arabic and English was warm and surprisingly intimate. The leader put the phone down. "Well," he shrugged, "apparently they're too wrapped up in internal affairs and the Syrian incident [referring to an Israeli airstrike on a Syrian military site a week earlier] to engage in open confrontation with the resistance factions."

But three days later Israeli politicians were still calling for revenge against Hamas for the rocket attack and, fearing assassination, the leadership had gone underground. All senior figures were in hiding and many of Gaza's Hamas-run police stations had emptied in anticipation of rocket strikes. So the dinner was held in one of Gaza City's many safe houses.

We were greeted by a lean young fighter - the leader's son - and two others of a similar age who put their Kalashnikovs aside to tend to dinner. The leader and I, plus an Australian journalist, sat on the floor and his son brought out cutlery and glasses and a large plate of chicken and rice, hastily prepared by a nearby restaurant. His wife called to confirm he wasn't coming home for dinner.

As we sat around the large plate, tucking in with our spoons and hands, the conversation quickly turned to security. The leader talked about the difficulties of being a senior member of one of the most monitored organisations in the world: "It has got harder as the technologies have improved." He talked candidly about the movement's hidden leadership, operating alongside the public one: "They remain secret for as long as they can and when they're uncovered, then they become public. After that, what can we do?" And he expressed hope that next year's US elections might bring some shift in US policy: "I hope the new administration will bring less ideological men to the table," he said.

After washing down our dinner with 7-Up, we moved from the floor to the main sitting room, where the leader reflected on his early days with the group of friends that would later form Hamas. He described how many of the Hamas leaders as young men had been leftists and Arab nationalists in the heady days of Gamal Abdel Nasser, but after the defeat of 1967 and Israel's occupation of the West Bank and Gaza, many of the Palestinians had become disillusioned and began to look to the work of the Muslim Brotherhood.

This group of men, then part of a community of Palestinian intellectuals working and studying in Cairo, grew more and more convinced by the Muslim Brotherhood's dream of a Middle East governed by Islam, and the abolition of the colonial boundaries imposed by the Sykes-Picot agreement by which the Ottoman empire was divided up among the French and British after the first world war. "We were the first of the new generation of Islamists," he said. "We believed that Islamic revolution in a neighbouring country would come and a new Islamic state would help us liberate Palestine." He welcomed democracy. "If real democracy was applied tomorrow, the whole region would be governed by Islamists," he said.

As we spoke, the man's son and fellow fighters sat in the corner behind the small of the wall eating and chatting among themselves, walkie-talkies and Kalashnikovs nearby. "Things were very different then," said the leader, describing the west's fear of political Islam today. "Our convictions are the same but the perceptions have changed. In the 80s, Bin Laden and the mujahideen in Afghanistan [then fighting against the Soviet Union and its occupation of Afghanistan] were hailed by Reagan as great freedom fighters. They were received in Europe and America."

He recounted being with Sheikh Abdullah Azzam - a leader of the CIA-backed Afghan-Arab jihadists who had been a central influence in Bin Laden's early years and was assassinated in 1995 - at a public fundraiser in New Jersey one night in the 1980s, when they raised $250,000 for the mujahideen in Afghanistan.

The leader's son brought in syrupy pastries and a white fruit pulp. In the background the first Ramadan celebrations could be heard. Before long the slow clatter of fireworks had grown into an eruption of explosions. "I hate those things," he said, as they snapped and crackled in the background.

At that moment, there was a loud knock at the door. A second member of the leadership burst in, tailed by bodyguards, immaculate in his pristine white jellaba. We stood up to greet him.

Whereas our host took the more pragmatic line within Hamas, the new guest was more militant. Before long the conversation turned to Hamas's refusal to recognise Israel and then to the group's aim for the destruction of the Jewish state, or what they would describe as the replacement of Israel and the occupied territories with one democratic state for Jews, Muslims and Christians. These men understood the need for a two-state solution, but only as a stepping stone to one eventual state.

"Switzerland is the model," the pragmatist said with certainty. "They killed each other for 200 years and now they live together peacefully." Unwilling to accept the possibility of two states living side by side in peace, he insisted that binationalism in the entire area of Israel and Palestine was the only solution - "One state for two peoples." He outlined the Swiss experience, enthusing over the potential for a state made up of localised cantons of control where all citizens would hold a common passport but would have to respect the individual laws and governance of each canton. "We believe there is a historical precedent for friendship between Jews and Muslims. We can live together again."

At this, the other leader interrupted. "With all due respect to my friend, the Palestinian people will never accept it." As the hardliner talked, the moderate sifted through a bowl of Chinese crackers with a frown, picking out his favourite pieces. "We need a single democracy on our terms. The Jews can live as individuals in a Palestinian state protected by our laws," said the more militant leader.

The pragmatist defended his optimism. "This is just the culture - people have been raised on a different rhetoric - but if you explain it to the people, they will accept it." The hardliner retorted: "This land is not fit for two sides, the cantons will not work. Anyway, any such idea will collide with the Israeli mentality."

Watching this conflict within Hamas, it seemed clear that this fundamental difference in vision at the helm of the movement would return again and again. But despite their differences, both men seemed convinced that Israel as a Jewish-only state was in decline. Citing articles in the New Yorker, Foreign Affairs and the New York Review of Books, they described a growing debate about "post-Zionism" - a school of thought within Israel that believes that Zionism as an ideology has served its purpose and that the Jewish state should now move towards becoming a secular democracy. "Take Avraham Berg [a former speaker of the Israeli Knesset] for example," said the hardliner. "He's talking about post-Zionism and the fall of the Jewish state if it continues to be purely Jewish. And it is not just leftwing Israelis; it's now acceptable for people in the west to think about, and talk about, a world without Israel."

Echoing a conversation he had earlier in the week, the hardliner outlined his strategy for defeating Israel. "The Gaza withdrawal was a victory," he said. "For us, any withdrawal equals a retreat. The Israelis were forced to give up territory - there was a time when no one believed that could happen." He described how the wall, the gigantic separation barrier erected by the Israelis and the source of so much anguish for West Bank Palestinians and the besieged population of East Jerusalem, was also viewed as a success. "The wall was a limitation on the expansion of the Israeli state. For years the Israeli right had talked about a Greater Israel stretching from the Nile to the Euphrates. The wall has brought an end to that dream."

He said that Hamas is focusing on two aims: "To limit the expansion of Israeli territory, and to wear down the occupation by making it too expensive to continue. If we stay on this course, in another 50 years we may have our land back."

When the time came for me to leave, the two men wished me a safe journey and urged me to come back."I hope we will see you again soon," said the hardliner. "If I am not martyred before then," he added with a smile. As the same Mercedes that had picked me up shuttled me back through the dark, empty streets to my hotel, I wondered if the threatened airstrikes might indeed claim his life before my next visit to Gaza.