Israel is examining a Hamas truce proposal delivered by Egypt, defense officials said, but violence persisted Friday as a Hamas militant was killed in what the group said was a clash with Israeli troops near the Israel-Gaza border.

Israeli calls for cease-fire talks with the militant group that rules the Gaza Strip grew Friday as an Israeli Cabinet minister said he supported such negotiations under certain conditions.

A Hamas official implied the offer was part of the Islamic group's efforts to reach out not only to Israel, but also to Palestinian President Mahmoud Abbas, who has controlled only the West Bank since June when Hamas ousted his Fatah party's security forces from Gaza.

Since the Hamas takeover, Abbas has rejected offers by the group to talk, insisting Hamas must first step down in Gaza. Israel has also refused to do business with the militant group, and has virtually closed all crossings with the impoverished area where 1.5 million Palestinians live, allowing in only food and humanitarian aid.

Earlier this month, Israel and Abbas' administration began the first official Israeli-Palestinian negotiations in almost seven years. But the question of what to do with the Gaza Strip plagues the negotiations on a final peace agreement, which the sides hope to complete by 2009.

Israeli defense officials, speaking on condition of anonymity because of the sensitivity of the issue, said Thursday the Hamas offer was limited to stopping the rocket fire in exchange for a halt to Israeli military operations in Gaza.

They said Hamas gave assurances it could impose the truce on the militant groups that are firing the rockets — Islamic Jihad and the Popular Resistance Committees.

Israeli Infrastructure Minister Binyamin Ben-Eliezer said Friday that Prime Minister Ehud Olmert may consider talks with Hamas on a long-term cease-fire. But, as part of such a deal, Hamas must also cease smuggling arms into the Gaza Strip and open talks for the release of an Israeli soldier, Cpl. Gilad Shalit, captured by Hamas-affiliated militants last year, Ben-Eliezer said.

"The prime minister I know doesn't totally rule anything out," Ben-Eliezer told Israel Radio. "If a serious, realistic proposal is put on the table and Hamas is willing to discuss a long-term cease-fire and is willing to stop the terror, to stop the smuggling and is willing to open talks on the release of Gilad Shalit, I would go to negotiations."

Olmert's office reiterated Friday that Israel is not currently holding talks with Hamas and would only consider them if the militant group renounces violence, recognizes the Jewish state and accepts peace agreements.

Hamas official Salah Bardawil said the offer by Hamas leader Ismail Haniyeh was part of the group's general policy to close the rift with Israel and would have to include talks with Abbas as well.

"All the Palestinians are in a crisis; not Hamas," Bardawil said. "We are not lovers of war. We love our rights. If we can get them through a truce, that would be an achievement."

Hamas spokesman Sami Abu Zuhri said the group had not yet seen any sign that Israel wants a truce.

"To this minute, what we see is Israeli aggression," Abu Zuhri said after at least six Palestinian militants were killed in clashes with Israeli troops on Thursday. "The occupation (Israel) is proving that it is not interested in any truce."

Violence continued Friday. A Hamas militant was killed by Israeli troops near the Israel-Gaza border, the group and medics said. The Israeli army spokesman's office said it was not aware of any clashes in the area.

Late Thursday, Hamas said it fired three rockets at Israel, its first such claim in weeks, putting the truce talk in doubt.

Abu Obeida of the Hamas military wing said the target of the rockets fired by Hamas was an Israeli military base. "This is a tactic of the Hamas military wing," he said. "It has nothing (to do) with a truce or escalation."

Hamas first floated the idea of a truce earlier this week when Haniyeh called an Israeli TV reporter. Previous truces have been negotiated through Egyptian mediation, but none have held for long.

On Friday, Haaretz newspaper reported a confidant of Olmert has gathered majority support in parliament for a bill that would compensate Jewish settlers in the West Bank who move before Israel withdraws from some areas as part of a peace agreement with the Palestinians.

The effort by Vice Premier Haim Ramon is meant to prevent forcible evacuation of tens of thousands of settlers from the territory. In Israel's withdrawal from the Gaza Strip in 2005, Israeli forces had to physically remove most of the almost 9,000 settlers living there.

Israel hopes to hold on to some parts of the West Bank, where 270,000 settlers live, so it is unclear how many will be forced to leave.