JERUSALEM — Prime Minister Olmert and the Palestinian Authority president, Mahmoud Abbas ,met yesterday for the first time in six weeks, as the two leaders sought to make inroads on American-sponsored peace talks in advance of President Bush’s visit to Israel in May.

Mr. Bush will help commemorate Israel’s 60th anniversary. His administration is making a strong push for Israelis and Palestinians to achieve a lasting peace settlement before he leaves office early in 2009.

Messrs. Abbas and Olmert met for two hours along with their senior negotiating teams, then conferred one-on-one for an additional hour.

A senior Palestinian official, Saeb Eerekat, who attended the negotiating sessions, characterized the discussions as “in-depth and serious,” and said the two leaders hoped to meet again in about two weeks.

Neither side would provide details of yesterday’s discussions, which were expected to address the core issues that have derailed previous attempts at a lasting peace. These include the potential division of Jerusalem, the fate of Palestinian refugees and the final borders of an independent Palestinian state.

“If our talks with the Palestinians are going to succeed, there has to be a high level of discretion,” a spokesman for the Israeli government, Mark Regev, said.

Since the American-sponsored peace conference in Annapolis, Md., in November kicked off the current negotiating push, talks between the two sides have been frequently challenged by events on the ground. Mr. Abbas briefly suspended the sessions in April after more than 100 Palestinians, many of them civilians, were killed during an Israeli incursion in the Hamas-controlled Gaza Strip.

Each side has regularly accused the other of violating terms of the “road map,” peace plan which requires Israel to halt settlement construction in the occupied West Bank and charges Palestinians with reining in militant groups.