The trip by Ehud Olmert takes place shortly after the US vetoed a UN security council resolution condemning an Israeli attack that killed 18 civilians in Gaza on Wednesday.
A midterm US election last week showing deep popular dissatisfaction with the war in Iraq has also raised speculation in Israel that Bush could try to cap his two-term presidency with progress on Israeli-Palestinian peacemaking.
Olmert flew in on Sunday night and is to meet Bush on Monday to discuss Israel's conflict with the Palestinians and Iran's nuclear programme.
Before leaving Israel, Olmert said: "It is the right time ... to exchange views with the president on what is expected in the coming two years.
"The main subjects will be the situation in the Middle East and the Iranian issue."
Talks are expected to focus on Tehran's nuclear programme which the US says could lead to the development of atomic weapons.
Israel, which is widely believed to be the only country in the Middle East to have nuclear weapons, says that Iranian threats to destroy Israel should be treated seriously.
Olmert said the Palestinian issue would also be on the agenda.
"There is no way we can ignore it," he said at the weekend. "We have to find the best partner."
Arab League conference
Olmert's visit to Israel came as the Arab League said that it would hold a peace conference to be attended by major UN powers, Arabs and Israelis.
Mahmoud al-Zahar, the Palestinian foreign minister, whose Hamas organisation heads the Palestinian government and calls for the destruction of Israel, declined to say whether the group would attend the proposed peace conference.
"Will this conference be held or not? What's the agenda of the conference? We don't know. I leave this matter to the future," he said.
Mark Regev, the Israeli foreign ministry spokesman said that Israel welcomed the proposed conference.
However he also said that Israel would not negotiate with Hamas unless the Palestinian group dropped its calls for the destruction of Israel.
"A multilateral conference doesn't make Hamas legitimate," Regev said.
"What makes Hamas legitimate is accepting the international benchmarks."
The Arab League has not said when the conference would be held.