JERUSALEM — The Israeli and Palestinian prime ministers met here for a second time Thursday night to air their disagreements over how to pursue a new international peace plan, inching toward concessions and polishing their images as peacemakers before a summit meeting next week in Jordan with President Bush.

Each side emerged from almost three hours of talks proclaiming itself encouraged. Mahmoud Abbas, the Palestinian prime minister, reiterated his intention to put a halt to violence, officials said, while Ariel Sharon of Israel promised an easing of restrictions on Palestinians.

There were no immediate signs of action on the most politically fraught demands of the new international peace plan known as the road map, like Palestinian collection of illegal weapons or Israeli restraint of settlements in the West Bank and Gaza Strip.

But in response to a Palestinian demand for the release of prisoners, which is not called for in the plan, Sharon told Abbas that he would free 100 detainees, officials said. He also said that Israel would speed up the release of Palestinian funds sequestered by Israel during the conflict and that it would lift heightened restrictions imposed earlier this month on Palestinian travel from the West Bank and Gaza Strip.

Israel will also permit more Palestinian goods and workers to cross the boundaries of the West Bank and Gaza, Israeli officials said.

Israeli officials said that Sharon told Abbas he would look into another Palestinian request, reopening the Palestinians' airfield in the Gaza Strip, which was closed and then scored with trenches by the Israeli army during the 32-month conflict.

As a late-spring sandstorm lashed Jerusalem, the leaders met over dinner, at a time of fragile hope for stemming the violence and going to work on the core disputes of the two peoples. Both have spoken recently in politically risky terms of aggressively pursuing peace. But after weeks of jockeying, they are only now coming to the substance of enacting the peace plan.

The leaders agreed to meet again, and to have deputies meet on specific issues, before wrapping up just before midnight Thursday. In a statement, Abbas called the meeting "serious, candid, and beneficial," and added, "The time is ripe for both Palestinians and Israelis to take the opportunity to make peace."

Each side appeared eager to signal to President Bush that it was doing its best to advance the plan.

Before sitting down with Sharon at his office Thursday night, Abbas told an Israeli newspaper that he expected to reach an agreement next week with the militant group Hamas to "stop terrorism" against Israelis.

But he said he would need help from Israel, citing a release of prisoners and a halt to military operations. He pressed Thursday night for those concessions, along with an end to Israel's targeted killings of suspected militants, Palestinian officials said.

Sharon repeated his demand that Abbas first take decisive action to stop terrorism, Israeli officials said. When the Palestinians acted, he said, Israel would suspend its military actions, a senior Israeli official said. But the official said that Sharon also warned that if Abbas relaxed his efforts, the army would return.

"It was loud and clear, said by the prime minister," the official said.

Sharon repeated a previous offer to withdraw forces from the Gaza Strip and from the centers of West Bank cities as Palestinian security forces took over. Abbas was said to have told him the Palestinian security forces were ready to go to work in Gaza, but were too weakened elsewhere by Israel's raids to be effective now.

The Israeli government reluctantly accepted the steps of the peace plan on Sunday, but Israel is still seeking significant changes in it, over Palestinian objections. The plan calls for rapid, reciprocal concessions to produce a Palestinian state and a comprehensive Arab-Israeli peace in three years.

A previous meeting between the two prime ministers, on May 17, revolved around Sharon's demand that Abbas act against violence and Abbas' demand that Sharon formally accept the peace plan.

Israeli officials have repeatedly rejected a truce with Hamas as insufficient, saying it would merely allow the group to rebuild. Instead, Sharon is demanding Abbas take five steps, a senior Israeli official said: arresting terrorists, confiscating weapons, dismantling the organizations, taking preventive measures and ending incitement to violence.

"Unless they do that, we can't move forward," the official said.

Hamas leaders said that they were still weighing Abbas' request for a cease-fire, which he delivered in a meeting with four Hamas men in Gaza City last Thursday evening.

"Right now there is nothing," said Dr. Abdel Aziz Rantisi of Hamas, one of the four. "We are studying the current situation. We are taking into consideration the changes in the region. Definitely we're going to come out with a statement."

Dr. Mahmoud Zahar of Hamas, who also met with Abbas, said the group had to consider the views of many members. "We have to get the position of all these various channels that exist, inside jails, in the West Bank, in Gaza, abroad," he said.

Palestinian and Israeli officials say that, since the war in Iraq, Hamas has come under new pressure. Its sponsors in Iran and Syria have been threatened, while Israel stepped up its attacks on the group and Mohamad Dahlan, Abbas' security chief, began reconstituting some Palestinian security forces, with assistance from the Central Intelligence Agency.

In the meeting last week, Abbas asked the Hamas leaders to consider the regional changes and ask themselves if they would remain immune, a top Palestinian official said.

But the Hamas leaders said that they also secured a promise from Abbas that he would not use force against them. In the newspaper interview, with Yediot Ahronot, Abbas demurred when asked if he would use force against Hamas, as the governing Palestinian Authority did in 1996. "We are not going backward," he said. "A civil war — never."

Abbas' associates say that he simply lacks the standing now to take on Hamas. They fear that if security officers attempted to arrest Hamas gunmen or leaders, warning calls over mosque loudspeakers in Gaza would bring thousands of Palestinians into the streets to block them.

To gain popularity, Abbas is trying to secure tangible gains from Israel, such as a halt to its military operations.

Abbas demanded from Sharon that he lift Israel's siege on Yasser Arafat, the Palestinian leader. Israel wants to isolate Arafat and exclude him from the peace process, and he is not putting his weight behind Abbas' efforts. But on Thursday, Arafat told reporters he did not mind being left out of the meeting with Sharon or the summit with Bush. "It's not important who is gong to this meeting," he said of the summit meeting. "What is important is that our position won't change."

According to the peace plan, each side is supposed to make a declaration as a first step. Israel is supposed to affirm its commitment to an "independent, viable, sovereign Palestinian state" — a stronger formulation than Sharon has used in the past. At the same time, the Palestinians are supposed to issue a declaration reiterating Israel's right to exist in peace and calling for unconditional cease-fire.

Palestinian officials said that they expected those declarations to be made after the meeting with Bush, scheduled to take place Wednesday in the Red Sea port of Aqaba.

Sharon, who titled his autobiography "Warrior," is one of Israel's fiercest hawks, while Abbas, a refugee of the 1948 Arab-Israeli war, has staked out a demand for a Palestinian state in all the territory Israel occupied in the 1967 war.

Yet Abbas has told associates privately that he believes he can negotiate successfully with Sharon. In the meeting Thursday night, an Israeli official said, Nabil Shaath, the Palestinian foreign minister, told his Israeli hosts that Abbas said ten years ago that the Israeli with whom he would ultimately sign a peace agreement would be Sharon.