After meeting with Mr. Sharon at the White House, Mr. Bush said his commitment to Israel's security was "unshakable." Last week, the president called the fence a "problem" that could undermine efforts to build confidence between the sides; today he referred to it as a "sensitive issue" that he would continue to discuss with Mr. Sharon.

But the president also suggested that Israel do more to help the Palestinian people and urged Mr. Sharon to show restraint as the two sides each weigh difficult steps in advancing the latest peace plan.

The meeting was the eighth between the leaders at the White House, and they referred to each other by their first names, reflecting Mr. Bush's deepening involvement as a peace broker. 

But behind the cordial tones, both sent clear messages. Mr. Sharon signaled that he was unwilling to make painful compromises without more concrete progress by the new Palestinian prime minister, Mahmoud Abbas, in cracking down on terrorism. For his part, Mr. Bush indicated that his support for Israel required Mr. Sharon to show patience and flexibility. 

Mr. Bush, who met here last week with Mr. Abbas, praised Israel for having taken steps to ease tensions, including granting more work permits for Palestinians who want jobs in Israel and removing some roadblocks that had choked traffic. But he also signaled that he wanted more concessions from Mr. Sharon and, without referring to any specific issue, appeared to warn him against taking too hard a line.

"I encouraged the prime minister to take further steps to improve the daily conditions faced by Palestinians," Mr. Bush said. "I also urged the prime minister to carefully consider all the consequences of Israel's actions as we move forward on the road to peace."

Mr. Sharon praised Mr. Bush as a leader in the fight against terrorism and suggested that Israel, like the United States, would never compromise with "terror and evil." He made clear that in the Israeli view, the burden was now on Mr. Abbas to make good on his pledge to take action against Hamas and other groups that keep Israelis under the threat of attack. 

"We are thankful for every hour of increased quiet and less terrorism, and for every drop of blood that is spared," he said. "At the same time, we are concerned that this welcome quiet will be shattered any minute as a result of the continued existence of terrorist organizations which the Palestinian Authority is doing nothing to eliminate or dismantle."

The Israeli leader said he was confident that Mr. Bush would "act to ensure that the Palestinians put a complete stop to the threat of Palestinian terrorism."

Mr. Sharon made a point of saying that the relative calm "was achieved first and foremost through the uncompromising activity of the Israeli security forces," adding that the international peace initiative led by Mr. Bush had also helped. 

Addressing the question of outposts, or unauthorized settlements by Israelis in the occupied territories, Mr. Sharon said they "will be removed" as required by the latest peace plan. As he did last week when Mr. Abbas was in Washington, Mr. Bush signaled that he supported Mr. Sharon's position of meeting Palestinian demands for the release of prisoners by freeing only those who are not a threat.

But more than any other issue on the table today, it was the fence — also referred to as a wall or a security barrier — that illustrated the mistrust still permeating relations between Israelis and Palestinians. The structure, concrete in some places, wire in others, already wraps around portions of the West Bank and ultimately could be hundreds of miles long.

Israelis say the wall is a way of keeping suicide bombers and other attackers out, but it has been excoriated by Palestinians for pushing deep into what they consider their territory, dividing communities and penning them in. Even some Israeli commentators have raised questions about the usefulness of the barrier and about whether it is in effect creating new borders that give up land Israel would like to keep.

The fence is not referred to specifically in the latest peace plan, known as the road map. But it has increasingly come up in the last month as the United States mediates between the sides. On a trip to the region in June, Condoleezza Rice, the national security adviser, heard complaints about the wall from Palestinians, and passed them along to Mr. Sharon, who politely rebuffed her, American and Israeli officials said at the time.

On Friday, after meeting with Mr. Abbas, Mr. Bush raised the subject in remarks to reporters, and when questioned about it, said, "I think the wall is a problem," adding that he had already discussed it with Mr. Sharon. 

Mr. Bush said on Friday that it would be very difficult to develop confidence between Palestinians and Israelis "with a wall snaking through the West Bank."

Today, Mr. Sharon brought the subject up when the two leaders appeared before journalists in the Rose Garden, indicating he was willing to stand up to Mr. Bush on issues he considers vital to Israel's security.

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

When asked about the topic today, Mr. Bush said the best way to address Israel's security was to go after terrorist groups like Hamas that threaten Israel. 

"Therefore, I would hope in the long term a fence would be irrelevant," Mr. Bush said. He added that the fence was a "sensitive issue" and that he would continue discussing it with Mr. Sharon. 

Speaking to reporters late today, an Israeli official said his country was willing to take steps to make the fence "less harmful" to the Palestinians, perhaps by opening more gates.