What appeared to have been a decision by Egypt and Saudi Arabia to cooperate with Hamas rather than with the Palestinian president, Mahmoud Abbas, in allowing 2,000 people to leave Gaza last week for a pilgrimage to Mecca is causing friction in Palestinian, Israeli and Western circles.

Some officials said the move was an insult to Mr. Abbas, a moderate. Only two weeks ago, Egyptian, Saudi and other international representatives gathered in Annapolis, Md., to support him and the embryonic Israeli-Palestinian peace efforts.

The pilgrims crossed directly from Gaza, which is under Hamas control, into Egypt, through the Rafah border terminal. From Egypt, they traveled on to Saudi Arabia, where the pilgrimage, called a hajj, is to take place this month.

An Israeli security official said Monday that Hamas and the Abbas-led Palestinian Authority had been preparing alternative lists “for weeks” to fill the Saudi quota set for pilgrims from Gaza. Israel had been coordinating with the authority to let more than a thousand pilgrims leave Gaza via the Erez crossing in northern Gaza. From there, they were to travel through Israel and the West Bank into Jordan, and on to Saudi Arabia. Thousands more Palestinians from the West Bank left separately, officials said.

Palestinian officials close to Mr. Abbas are trying to play down the issue. But one Abbas aide said, “People here felt stabbed in the back.” Like some other officials on all sides, he spoke on the condition of anonymity because a delicate religious issue is involved.

The Rafah crossing in the south of Gaza has been officially closed since June, when Hamas seized control of the Gaza Strip in a brief factional war. Mr. Abbas, who leads the rival Fatah faction, has set up an alternative caretaker Palestinian government to govern from the West Bank. Hamas, which won parliamentary elections in 2006, does not recognize its legitimacy.

The Abbas-approved pilgrims were supposed to have left Gaza last Wednesday and Thursday. Instead, Israeli and Palestinian officials confirmed, 2,000 pilgrims crossed through Rafah in the two days before. Most of those on the Abbas list were left behind in Gaza, they said.

Israeli officials said they had been told by Egypt that the Palestinian pilgrims had broken through the border, and that Egyptian border guards had no choice but to let them in to avoid violence. A prominent Hamas leader in Gaza, Mahmoud Zahar, backed the Egyptian version of events, denying any prior coordination.

But Israeli officials doubted that was the case. “They needed visas from Saudi Arabia, which required prior coordination,” the security official said.

The pilgrims who left through Rafah included some prominent Hamas members.

Nimr Hamad, a political adviser to Mr. Abbas, tried to minimize the damage. The Palestinian Authority did not want “to turn a religious issue such as this into a problem,” he said. “For some, the pilgrimage is like going to paradise. It is sensitive.”

But Mr. Hamad acknowledged that he had expected that “those leaving would be coordinated” through what he called “the legal leadership” in the West Bank. Instead, “Hamas tried to impose” and coordinated the Gaza pilgrims’ departure, he said.

On Monday, the minister of religious affairs in the Abbas government, Jamal Bawatineh, said he was in contact with Saudi officials to try to solve the problem of 910 pilgrims left behind in Gaza, as well as some other registered pilgrims who had remained in Jerusalem and the West Bank.

The Egyptians and Saudis may have been trying to exert subtle pressure on Mr. Abbas. Both countries are known to favor a resumption of dialogue between Hamas and Fatah. The Saudi-brokered Mecca agreement last February paved the way for several months of power sharing between Hamas and Fatah.

A Hamas spokesman in Gaza, Sami Abu Zuhri, said Monday that Egypt and Saudi Arabia had been trying to arrange a meeting between Hamas and Fatah. Mr. Abbas has refused any talks with Hamas, though, until it retreats from its takeover of Gaza.

Israeli officials said they had raised concerns with Egypt over the passage of the pilgrims through the Rafah crossing, saying it was just one example of Egyptian laxity at the border.

Mark Regev, a spokesman for Prime Minister Ehud Olmert, said, “We are concerned that extremist elements are exploiting the situation along the border, and call upon all parties to do more” to maintain security there.