President Bush is using a blunt word, “occupation,” to describe Israel’s presence in the West Bank, as he predicts that a peace treaty between Israel and the Palestinian Arabs “can happen” by the end of 2008 — a date that essentially coincides with the scheduled end of his presidency.

Consecutive American administrations have considered the West Bank and Gaza “occupied” territories, and Ariel Sharon used the term as well when he was prime minister. But Mr. Bush’s remarks and peace prediction yesterday, at the conclusion of his first trip to Jerusalem as president and his first visit ever to Ramallah and Bethlehem, were seen as part of a term-ending diplomatic push with potentially dangerous consequences for Israel and the region.

The Israeli press also seized on a separate reported remark made by Mr. Bush at a dinner in Jerusalem last night, imploring government ministers to support the dinner’s host, Prime Minister Olmert, and assure he remains in office, which only underlined the political dimension of the presidential visit.

Mr. Olmert faces a potentially scathing report by the Winograd Commission investigating the 2006 Lebanon War, which is expected to publish its final conclusions at the end of January. The report will concentrate on the last few days of the war, where in the view of critics many Israeli soldiers were killed because of bad decisions taken by Mr. Olmert’s government. The Palestinian Authority under the leadership of President Abbas is fragile as well, and Mr. Bush’s last year is expected to be overshadowed by the stretched out presidential race.

Peace negotiators of the Clinton era are familiar with the “temptations of the ticking clock,” said a Woodrow Wilson Center scholar, Aaron David Miller, whose new book, “The Much Too Promised Land,” describes his experience as a top American negotiator between Israel and the Palestinian Arabs in the last year of the Clinton Administration. The diplomatic collapse at that time led to renewed violence. By moving too fast and “overreaching,” Mr. Miller said, the Clinton administration ended up “undermining the prospects of hope.”

He added he now believes in a “diplomatic Hippocratic Oath,” which would stress doing no harm. “There should be an end to the occupation that began in 1967,” Mr. Bush said yesterday, as he delineated the contours of a peace agreement in remarks to the press at King David Hotel in Jerusalem. “The agreement must establish Palestine as a homeland for the Palestinian people, just as Israel is a homeland for the Jewish people.” A peace agreement “should happen, and can happen, by the end of this year,” he added.

Israeli commentators said Mr. Bush probably tried to “offset” his description of Israel as a “Jewish state” – which is strongly resisted by Palestinian Arabs and the rest of the Arab world – by bluntly using the term “occupation.” But they were mostly concerned about his push for quick agreement signing. Saying he understands that the Palestinian Arabs do not want their state to look like “Swiss cheese,” Mr. Bush told reporters in Ramallah yesterday that Israelis “don’t want a state on their border from which attacks would be launched.”

“What are they talking about?” said a former top adviser to Mr. Sharon, Chuck Freilich. “Not a day goes by without rockets on Sderot. A few days ago, rockets fell in Ashkelon. Last week we intercepted preparations in Gaza for launching rockets that could hit the Tel Aviv area. Sooner or later — it could be five minutes, five days, a year — such rockets will hit a major Israeli population center, with many casualties. And here, everybody is talking about peace.”

President Bush met yesterday with the opposition leader, Benjamin Netanyahu of Likud, who leads polls as Mr. Olmert’s most likely successor. If Israel loses control over Jerusalem’s holy sites, Mr. Netanyahu told his guest, they will be taken over by Islamists who will deny access not only to Jews but also to Christians, according to Likud’s top foreign policy adviser, Zalman Shoval.

“Like Tony Blair,” Mr. Netanyahu “believes in economic peace,” Mr. Shoval said. The only way to move institution building among Palestinian Arabs, he told Mr. Bush, is to create a private enterprise-based economy in the territories. “Too bad we had a Paris donor conference,” Mr. Shoval said, referring to a recent international gathering there in support of Mr. Abbas. “Let’s hope the next one is a business conference.”

Prior to developing a viable, market-based economy, and to creating sound institutions, Mr. Shoval added, agreements with the current Palestinian Arab leadership could do more harm than good. “Signing any agreement now could be a terrible mistake for Israel,” he said. “Even if it takes years to implement, anything Israel gives away now would serve as a starting point for future negotiations.”