The nights in Gaza belong to the Izzedine al-Qassam brigades. On potholed streets in the border city of Rafah last week, disciplined rows of fighters bristling with guns and rocket launchers listened to a midnight pep talk from their commander before melting into the darkness.

The militia that was once the underground military wing of Hamas, the Islamic extremist organisation, has become a feared unofficial army controlling this isolated strip of Palestinian territory.

The Qassam commander, a fighter wanted by the Israelis, sent them into the winter rain with exhortations to “remember that God is with you” and “don’t fall asleep”. Every night they patrol the streets and the border with Egypt, looking for wayward citizens and ever ready for Israel to invade. The streets are deserted. Gazans fear these men.

The most impressive thing about Qassam is its armoury. Each six-man unit travels with rocket-launchers, machineguns and grenades and carries a locally made antitank mine similar to the explosively formed projectiles (EFPs) that have wreaked havoc against allied armoured vehicles in Iraq.

With Qassam and the Hamas police patrolling Gaza since secular members of the Palestinian Authority were driven out in June, there are no more of the unpredictable gun battles that once made the streets so lethal.

But this Hamas-imposed security has come at huge cost. Only believers feel safe; supporters of Fatah, the political organisation led by Mahmoud Abbas, the Palestinian Authority president, are routinely arrested and tortured. Journalists are harassed and unIslamic dress can result in a beating as well. More and more women in Gaza are covering not just their hair but their faces. Many bitterly resent Hamas.

Gaza is growing more and more isolated. Israel controls the borders, land and sea, and has closed the crossings since June. Food prices have rocketed, unemployment is at 70% because no materials can be imported and nothing can be exported. Israel cut fuel supplies last month and has said it will cut electricity supplies from Sunday.

In the latest sign of its total international isolation, Hamas, although democratically elected in 2006, has been excluded from the Middle East peace conference in Annapolis, Maryland, on Tuesday.

The organisation’s isolation comes from its refusal to recognise the existence of Israel, renounce violence or abide by any agreements signed between Palestinians and Israel. Yet it remains defiant.

Abu Atiya, the Qassam leader, said after reviewing his troops just after midnight: “Abu Mazen [the familiar name for Mahmoud Abbas] can sign anything he wants. We will not obey any agreement that does not give Palestinians their rights.”

He added a warning to Abbas, who fired the Hamas government after the June coup in Gaza. “If he tries to return by force, we will fight him.”

Nonetheless there were other signs last week that the divide-and-rule tactics of Israel and the West – to strengthen Abbas by showing that he can make political and economic gains while life worsens under Hamas – may be working for the first time. One Hamas leader said: “I have told the leadership the takeover of Gaza was a mistake. We have no strategy, we are just reacting to events. It was a big loss for us to attack and criticise Abu Mazen and let him fly away.”

He added that Hamas was now isolated from Arab countries, too. The pragmatists, he said, accepted that a solution must involve two states, Israel and Palestine – a heresy in the extremist Islamic group. “Hamas is not prepared for the political game they have to play,” he said mournfully. “They see resistance, only resistance.”

The pragmatists worry that support for Hamas – which won elections overwhelmingly in 2006 – is waning in Gaza, its stronghold. Every victim of its repression fuels the growing anger.

One of the most recent, Ibraham Abu Taha, 24, lay in a bed at Al Quds hospital in Gaza City last week after Hamas forces clashed with demonstrators marking the third anniversary of the death of Yasser Arafat, the Palestinian leader. Taha, who married two months ago, held a finger over his tracheotomy tube so he could talk and said: “They started shooting. One grabbed me by my keffiyeh [headscarf], and I tried to run. He shot me.” Eight died and at least 100 were injured by bullets or beatings.

Islamic fundamentalism has also begun to grate for many who may once have supported Hamas. Courts are now being convened in mosques, based on sharia (Islamic law).

Last week two university students were taken to court for having a romance. The court tried to force them to marry but their feuding families refused. In the end, the court ordered the woman’s family to keep her at home and her boyfriend to leave the city for a year.

Anger is growing – at the Israelis, at Hamas and at the sense of being trapped in a prison with 1.4m inmates. This desperation may fuel extremism, just when there is the first glimmer of hope for peace in years.

“At least in prison, and I’ve been in prison, there are rules,” said Raji Sourani, director of the Palestinian Centre for Human Rights. “But now we live in a kind of animal farm. We are penned in and they just dump in our food and medicine.”