(Updates with new air strike)

By Nidal al-Mughrabi

GAZA, May 25 (Reuters) - Palestinian militant groups behind rocket attacks on Israel signalled softer terms for a truce on Friday, but Israel renewed strikes on Gaza targets, including a guardhouse outside the home of Prime Minister Ismail Haniyeh.

Hospital officials said three passersby were wounded in strikes on a home and a wood shop in Jabalya refugee camp. Another missile destroyed a caravan used to house Haniyeh's bodyguards near his home in Gaza City, but no one was hurt.

The new strikes could derail Palestinian President Mahmoud Abbas's efforts to persuade militants to stop firing makeshift rockets at Israel.

Hamas and other factions had earlier signalled readiness to consider a proposal by Abbas that would effectively lead to renewing a Gaza ceasefire that the moderate leader and Israeli Prime Minister Ehud Olmert declared in November.

"The next 48 hours will be decisive for determining which way the factions are going, and it will depend on Israel and whether it wants to stop its aggression," said Abdel-Hakim Awad, a spokesman for Abbas's Fatah faction. But the militants denied that any commitments had been made, saying only that they were weighing a proposal made by Abbas for a trial month-long truce in Gaza.

"Our position is that a ceasefire must be mutual, simultaneous and reciprocal and it must cover Gaza and the West Bank in the same time," said Hamas spokesman Ayman Taha.

"Despite our position, we have told Abu Mazen (Abbas) that we will study his offer and inform him of our response in the near future," he said.

Militants had previously conditioned ending the attacks on Israel agreeing to a simultaneous ceasefire in the occupied West Bank. Israel had rejected such calls as a ruse.

Israeli officials were not available to comment on the reported progress in the internal Palestinian talks, which took place even as Israel pressed a campaign of air strikes.

Earlier on Friday, two Hamas militants died when missiles struck their car in the Gaza Strip, hospital officials said. Other strikes targeted positions used by Hamas and another group, Islamic Jihad.

ISRAEL KEEPS UP PRESSURE

During the current cross-border violence, Israel has rebuffed calls for a ceasefire, instead campaigning for international pressure on the Hamas-led government to back down. There has been talk of dispatching foreign peacekeepers to Gaza.

The November truce did not apply to the West Bank, where Israel has mounted frequent and often bloody raids. It has said the operations were needed to thwart planned militant attacks. April saw a spate of Israeli-Palestinian fighting in Gaza, which militants said was justifed by the ongoing West Bank clashes.

The new Palestinian truce efforts underscore the precariousness of a power-sharing deal between the governing Hamas Islamists and Abbas's rival Fatah, which only recently ended a spate of street battles stoked by political deadlock.

Abbas wants calm in hope of restarting peace negotiations with Israel, but cannot afford to appear an Israeli stooge.

Abbas has called the rockets "pointless" and "needless". A Hamas official, Nizar Rayyan, said before Friday's talks that "Abbas hates rockets just like we hate the Jews."

Hamas is aware that the latest fighting has deepened Palestinian rancour at the government, already crippled by a Western aid embargo imposed over Hamas's refusal to recognise Israel and renounce violence.

Israel's air strikes have killed at least 38 people, of which militant groups say 25 were fighters. Israeli troops also arrested the Palestinian education minister, who is from Hamas, and 32 other officials in the West Bank on Thursday -- a move that raised concerns in Washington and at the United Nations.

More than 150 rockets have been fired in the past two weeks, ending six months of relative calm. One killed an Israeli woman this week in the town of Sderot. On Friday, three Sderot residents were wounded by a rocket salvo claimed by Hamas.

Representatives of Fatah and Hamas may also meet Egyptian mediators separately in Cairo in the coming days, Palestinian and Egyptian officials said.

A Fatah delegation is due there on Saturday and a Hamas spokesman said it would also be prepared to meet Egyptian officials if a formal invitation was sent.

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