President Bush said Tuesday "tremendous opportunity" exists to make "tangible progress" in helping Israelis and Palestinians live side by side in peaceful states.

"I am encouraged by the positive steps that Israel has taken to ensure peace, including prisoner releases," Bush said after his eighth meeting in Washington with Israeli Prime Minister Ariel Sharon (search).

"Prime Minister Sharon is now meeting regularly with Prime Minister Abbas (search) and that's positive ... Israel has recently taken steps to make it easier for Palestinians to work in Israel and to travel to their jobs and schools and family and I thank the prime minister for these actions," Bush said.

Bush is continuing to push the road map for peace between Palestinians and Israelis that aims to allow two states to live side by side in peace and security.

The mideast leaders promised to implement elements of the road map during meetings in Sharm-el-Sheik, Egypt, and Aqaba, Jordan last month. On Tuesday, Sharon was in Washington to meet with the president and discuss measures Palestinians must take in order to satisfy its side of the bargain.

His message must have gotten through to the president. Bush said "terrorism can never be justified by any cause.

"The Palestinian Authority must undertake sustained, targeted and effective operations and confront those engaged in terror and to dismantle terrorist capabilities and infrastructure," he said, adding that he wants to help Abbas achieve that goal.

"My commitment to the security of Israel is unshakable," he said.

Sharon has argued that Israel has already torn down 10 of the major West Bank roadblocks and other barriers to Palestinian travel. On Monday, the Israeli Cabinet (search) agreed to release hundreds of Palestinian prisoners as a gesture of goodwill.

A senior Israeli official traveling with Sharon said about 540 prisoners would be released within a week — about 210 from the militant groups Hamas and Islamic Jihad, about the same number from Fatah, headed by Palestinian leader Yasser Arafat and Abbas, and the rest held as criminals.

The two groups and the Al Aqsa Brigades, a spinoff of Fatah, are responsible for most of the suicide bombings that have killed hundreds of Israelis in nearly three years of the latest Palestinian uprising.

For his part, Sharon said he remains concerned that the "peace process will be shuttered any minute as a result of the continued existence of terrorist organizations which the Palestinian Authority is doing nothing to eliminate or prevent."

The prime minister said he trusts that Bush "as leader of the free world" will take steps to make sure that terrorism "will never rear its head again."

"I wish to move forward with the political process with our Palestinian neighbors and the right way to do that is only after the complete cessation of terror, violence and incitement, full dismantlement of terror organizations and completion of the reform process of the Palestinian Authority," Sharon said.

Bush's meeting with Sharon follows one last week with Palestinian Prime Minister Mahmoud Abbas, who laid out several complaints about the Israelis, in particular their continuing to build a security fence around the West Bank, their slow dismantling of settlements in the West Bank and a last-minute land grab. He also said that thousands of prisoners must be released.

At the time, Bush said that he would never ask the leader of any government to release people involved in terror. He repeated that sentiment Tuesday.

Last week, Bush criticized Israel's plans to build the security fence, saying that it stifles efforts to build confidence between the two parties, something the two sides are supposed to be working on. Israeli officials say they're not inclined to drop the wall project, since the one built around Gaza more than two years ago has stopped suicide bombings that previously originated from there.

Officials say they will listen to the president's concerns, and they might make some changes.

"Those extremists cannot have free access to blow up the peace process," said Israeli Foreign Minister Silvan Shalom last week during a visit to Washington. "We know the concern of our friends, the Americans, and we consider what needs to be done with the fence in the future."

But Sharon said Tuesday that he was willing to discuss the issue as the fence's construction continues.

"The security fence will continue to be built with every effort to minimize the infringement on the daily lives of the Palestinian population," Sharon said.

"On the Israeli side the issue is all about security," U.S. Ambassador Dennis Ross told Fox News. "They don't need to build this fence if the terror and the violence that produced it go away. If the Palestinians are doing their job in that respect, then the idea of a fence becomes much less compelling.

"I think the issue for the administration is to ensure that the fence doesn't preclude or prejudge the ability to negotiate a two-state solution," Ross said.

During last week's meeting with Abbas, Bush publicly praised the Palestinian prime minister for his commitment to fighting terrorism, but privately pushed him to dismantle Hamas and Islamic Jihad, who so far have only agreed to a three-month cease-fire.

"I'm going to tell you point-blank that we must make sure that any terrorist activity is rooted out in order for us to be able to deal with these big issues," the president told Abbas at a joint news conference in the Rose Garden.

Officials note that dismantling the groups is a requirement of the peace plan. Sharon continued to push the idea that the president must not allow two kinds of terror — one that the United States says it will refuse to accept and must be dealt with and another, like that by Palestinian groups that is seen as a political cause that must be dealt with differently.

"That is certainly one of the issues that Prime Minister Sharon all along has tried to present to the president," Ross said.

But Bush also is trying to encourage Sharon to work harder to help Abbas realize his good intentions, Ross said.

"What the president is going to try to do is emphasize to Prime Minister Sharon that he must do more to create an environment where Prime Minister Abbas can be seen as delivering for Palestinians so it is seen that his way works and Arafat's doesn't," Ross said. "I think Prime Minister Sharon understands that, but I think he will say there is a limit as to what he can do until Prime Minister Abbas really begins to take apart the terrorist infrastructure that exists within the territories."

Fox News' Wendell Goler and the Associated Press contributed to this report.