Arab ministers are preparing an agenda for the leaders
US White House spokesman Ari Fleischer said President Bush believed Israeli Prime Minister Ariel Sharon and his government should give "serious consideration" to allowing the Palestinian leader to attend the Beirut meeting.
The BBC's Barbara Plett says the delay has pushed the final decision until the last possible moment.
Raanan Gissin, an aide to Mr Sharon, told the Associated Press news agency the decision would now be made "very close to the time of the summit", which begins on Wednesday.
Mr Bush also urged Arab nations "to seize the moment" at the summit on Wednesday, and support a Saudi-inspired land-for-peace deal with Israel.
But Mr Fleischer said Mr Arafat had not done enough to stop violence in the region - and that remained a condition for any meeting with US Vice President Dick Cheney.
Lack of time
The latest US-brokered talks between the Palestinians and the Israelis were supposed to have continued after Sunday's talks chaired by American peac envoy Anthony Zinni ended without agreement.
Both sides were meant to have given their answers to US ideas for bridging gaps over implementing a truce plan.
Israeli security sources said the Palestinians told them they had not had enough time to discuss the proposals, but US officials said only that the talks had suffered from a scheduling problem.
Arab leaders are themselves demanding Mr Arafat's attendance in Beirut, but the Israeli Government has yet to decide whether he will be allowed to leave his West Bank headquarters which are blockaded by the Israeli military.
The Arab League's Secretary-General Amr Moussa opened the preparatory meeting in Beirut on Monday by reminding all present that both the regional and the international situation were "critical".
High on the agenda will be suggestions for Middle East peace proposed by Saudi Arabia which could amount to a "collective peace treaty" between Arab states and Israel, one official said.
Arab proposals
A draft text of the plan to be presented for approval by the heads of state calls for Israel and its citizens to accept the peace proposal to enable Arab states and Israel to co-exist peacefully.
Specifically, the Council of the Arab League wants Israel to:
In return, the Arab states would:
The peace plan will be discussed whether or not Mr Arafat is allowed to leave Ramallah, but the Arab leaders are taking a tough line.
Bahrain's King Hamad bin Issa al-Khalifa said it would "not be useful" if the Palestinian leader was absent.
Lebanon's Foreign Minister Mahmud Hammud said: "We want peace not surrender.
"We will not accept anything less than regaining our firm rights."
There has been quiet and cautious optimism about the Saudi plan from the international community, including Israel, though violence continued on Monday with Israeli tanks active in Palestinian areas.