Israeli Prime Minister Ehud Olmert asked Egypt’s intelligence chief yesterday to tell Gaza fighters a truce would be conditional upon progress being made toward freeing a captive Israeli soldier.

Olmert also asked Omar Suleiman to tell the Palestinian armed factions they would have to stop smuggling arms into Gaza if they want Israel to accept the Egyptian-brokered proposals to halt the violence in the besieged territory.

Suleiman was in Israel to seek the support of the country’s leadership for the truce plan, which already has Palestinian backing. In his talks with the Egyptian official, Olmert linked any truce to “progress in the negotiations for the release of Gilad Shalit,” captured by Gaza militants in a 2006 cross-border raid, a senior Israeli official said.

“The prime minister asked Suleiman to obtain the response of the Palestinian factions to the conditions,” the official said on condition of anonymity. Unless he receives a positive response, Olmert will not convene his powerful Security Cabinet to discuss and vote on a truce.

“These are indispensable elements in any quiet,” government spokesman Mark Regev told AFP. Both sides generally use the words “quiet” or “calm” to describe the proposed truce.

Defense Minister Ehud Barak earlier met Suleiman at his Tel Aviv residence and said Israel would respond to any attack from the Hamas-ruled Gaza Strip. “Barak made it clear that Israel will be unable to tolerate the continuing terror activity and fire from the Gaza Strip, and gave his assessment that Israel will have to launch a broad operation in Gaza if the rocket and mortar fire does not end,” Barak’s office said in a statement.

He too linked any truce to progress in the negotiations for the release of the Israeli serviceman. “Israel sees the release of Gilad Shalit and immediate progress in the negotiations on his release as a key component in normalizing the security situation in the Gaza Strip,” the statement said.

Hamas has demanded that Israel free hundreds of Palestinian prisoners in exchange for Shalit, but Egyptian-brokered negotiations on the details of an exchange have made little headway. Suleiman — Egypt’s point man for Palestinian affairs — has already secured the backing for the truce proposals of 12 Palestinian factions, including both the Islamist Hamas movement, which controls Gaza, and the secular Fatah group of moderate President Mahmud Abbas who holds sway in the West Bank.

Hamas has said the rocket fire will cease when Israel lifts its blockade of the impoverished territory and allows the reopening of border crossings, including the Rafah crossing with Egypt — Gaza’s only one that bypasses Israel.

In Gaza City, a senior Hamas leader, Mahmud Zahar, said any truce must require Israel to “stop all forms of aggression against our people and lift the blockade imposed on Gaza and the rest of the Palestinian territories.

“We hope that the Israeli side will listen to reason and put an end to its attacks and its blockade,” he told a news conference. But Zahar reiterated that there was no possibility of Hamas recognizing the Jewish state. “The first message we send to the Israeli side is and has always been that we will not accept any usurping entity on one inch” of historic Palestine, he said.

As Suleiman began his visit to Israel, two rockets fired from Gaza hit the southern port city of Ashkelon without causing any casualties. Islamic Jihad said it carried out the attack. The group, which has repeatedly fired rockets at Israel, has said that it will not sign a truce accord but will not stand in the way of one being implemented.

Hamas leader Ismail Haniyeh said he wished Suleiman success and called on Israel to “respond positively to the Egyptian efforts and to lift the siege and open the (border) crossings.”

In another development, public mistrust is mounting against Olmert, with an opinion poll yesterday showing a majority of Israelis think he should resign over a new probe into corruption allegations.

Fifty-nine percent of Israelis want Olmert to step down and 60 percent don’t believe his denial of any wrongdoing, according to the survey published by the mass-selling Yediot Ahronot newspaper.

“It is possible Olmert’s government will not finish its mandate,” Interior Minister Meir Sheetrit told public radio. Olmert’s term ends in November 2010, but there is increasing speculation he will be forced to step down or call early elections over the allegations he took bribes from a millionaire US financier.

Only 10 percent of the 500 Israeli adults interviewed for the Yediot poll thought Olmert was the best suited to be prime minister, with right-wing Likud party leader Benjamin Netanyahu getting the most support, with 37 percent. “The countdown for Olmert has started,” said political analyst Akiva Eldar.