Hamas plans to give its final response on Thursday to a proposed Egyptian-mediated truce, a senior official from the Islamist group said on Tuesday. Hamas lawmaker Salah Bardawil also said that Hamas is considering whether to accept a truce with Israel which would take effect just in the Gaza Strip.

The move would mark a significant concession by Hamas in dropping a demand that the truce immediately include the West Bank as well, as Egyptian mediators try to halt the fighting between Palestinian militants and the Israel Defense Forces in Gaza and southern Israel.

Bardawil said on Tuesday the group is now ready for a cease-fire that would begin in Gaza, and then move to the West Bank sometime in the future. He noted that Hamas is also considering a comprehensive truce for both territories as well.

For weeks, Hamas insisted on a mutual cease-fire in both the West Bank and Gaza Strip.

Bardawil also said a conversation with the Palestinian news agency Ma'an that a delegation led by senior Hamas official Mahmoud Zahar would present the group's response to the proposed cease-fire on Thursday, at a meeting with Egyptian intelligence chief Omar Suleiman in Cairo.

He added that, "If there will be resistance operations in the West Bank, the response to them will not be in Gaza, and Israel must accept this."

Bardawil noted that Hamas was willing to soften its stance to ensure the deal's success. He said Hamas' political leader, Khaled Meshal agreed to the proposal, indicating that all Hamas members, including its hard-line militant wing, must abide by the decision.

Israel regularly carries out air strikes and military incursions against Palestinian militants in Hamas-controlled Gaza, an area from which militants regularly launch rocket attacks on southern Israel.

While Israel is conducting peace talks with the rival Palestinian government in the West Bank, the Israel Defense Forces continues to carry out arrest raids in that territory as well.

Bardawil also noted that if Israel didn't abide to a truce in the West Bank as well, militants there could still legitimately carry out attacks.

Egyptian mediators initially suggested the proposal, Bardawil said.

Israel has repeatedly said it isn't negotiating with Hamas, a group that has carried out numerous suicide bombings and remains committed to Israel's destruction. A government spokesman said Tuesday that Israel would keep up its military pressure on Hamas as long as the group threatens Israeli civilians.

"Israeli defense measures are necessary because of the ongoing terrorism launched by Hamas-controlled elements in Gaza. If there were no terror activities there would be no need for Israel's military activity," spokesman David Baker said.

Also Tuesday, the Egyptian state-run newspaper al-Ahram reported Tuesday that Egypt and Hamas have drafted an agreement of principles on a cease-fire between the Islamist Palestinian group and Israel.

According to the report, Egyptian intelligence chief Omar Suleiman will soon present the outline of the agreement to officials in Jerusalem, and Hamas will soon present the agreement to Islamic Jihad officials for approval.

The Kuwaiti daily al-Rai reported that the agreement calls on Hamas to cease all resistance against Israel in exchange for Israel's lifting of an economic blockade on the Gaza Strip.

The exchange of prisoners, Palestinian prisoners held in Israeli jails and Israel Defense Forces soldier Gilad Shalit held by Hamas since 2006, will be postponed to a later date, the paper reported.

Egyptian sources told al-Rai that Israel has also demanded that Hamas put an end to the smuggling of weapons into the Gaza Strip.

Meanwhile, senior Israeli government officials have perceived a change in Hamas positions in recent days, at least concerning attempts to achieve a lull in fighting in the Gaza Strip. Nevertheless, Israel has not yet committed itself officially to a cease-fire and is waiting for a detailed proposal to be delivered via Egypt.

Israeli sources credit the turnabout in Hamas' position to the economic and military pressure put on Gaza.

Despite Hamas attempts to create a major incident at Kerem Shalom last Saturday, the IDF has made do with a limited reaction in Gaza, in part to prevent escalation during the holiday, but possibly also due to renewed Egyptian mediation.

Former U.S. president Jimmy Carter said Monday that Hamas is prepared to accept Israel's right to live in peace. Hamas is also prepared to accept the outcome of Israeli-Palestinian peace talks, provided it is approved in a Palestinian referendum or by a Palestinian government chosen in new elections, Carter said.

Carter was speaking following seven hours of talks with Hamas political leader Khaled Meshal in Damascus on Friday.

However, Meshal on Monday spoke of a Palestinian state on land captured by Israel in 1967 and said Hamas would not recognize Israel.

The Hamas leader said the group would "respect the Palestinian national will even if it was against our convictions."

Hamas officials have said before they would establish a peace in stages if Israel were to withdraw to the pre-1967 Six-Day War borders. But it has been evasive about how it sees the final borders of a Palestinian state, and has not abandoned its official call for Israel's destruction.

"They said they would accept a Palestinian state on the 1967 borders if approved by Palestinians ... even though Hamas might disagree with some terms of the agreement," Carter said in a speech, after talks in Syria and Egypt with Hamas leaders.

On Tuesday, Israel will open in a very limited way the Erez Crossing at the north end of the Gaza Strip, and probably also the Sufa Crossing. The Kerem Shalom Crossing will remain closed for now after last Friday's attack. The fuel terminal at Nahal Oz, where two civilians were killed two weeks ago, has been closed for a few days. It seems the Dor Alon fuel company, which operates the terminal, is worried about additional attacks.