Egyptian Vice President Hosni Mubarak met with high-level American and Israeli officials today, for the first time since the Tuesday assassination of president Anwar Sadat, for mutual assurances that the Middle East peace process begun under Sadat would be continued.

Mubarak, who is expected to take over the presidency following a national referendum Tuesday, met for 40 minutes this afternoon with Israeli Prime Minister Menachem Begin, and for half an hour with former U.S. presidents Jimmy Carter, Gerald Ford and Richard Nixon in an American delegation headed by Secretary of State Alexander M. Haig Jr.

Haig told reporters on the American delegation's plane, which arrived here this morning, that in the wake of the assassination the United States is preparing to speed deliveries of U.S. military arms to Egypt -- a subject broached by Mubarak during a visit to Washington two weeks ago.

He said he would urge Mubarak to sign a cooperation treaty with Sudan, Egypt's southern neighbor, to bolster the shaky pro-American government there of President Jaafar Nimeri.

The official Middle East News Agency said today that Mubarak had accepted an invitation from President Reagan to visit Washington, and it is expected that he will go there early next year.

Outside Cairo, police were reported today to have reestablished order in the still tense city of Asyut, 250 miles to the south, after battling yesterday and last night with armed bands of Islamic fundamentalists. Hospital and other local sources said 45 persons were killed in the fighting.

Deputy Prime Minister Fouad Mohieddine said the situation was "under control" and insisted there was no connection "at this stage" between Sadat's assassination and the insurrection in Asyut.

He said the government was taking "severe measures" to prevent the recurrence of such incidents. He also said that an explosion in the capital last night was a grenade that went off accidentally in a police barracks.

No other incidents were reported elsewhere in the country today, but security was noticeably stepped up in the capital as a multitude of official delegations began arriving for the funeral ceremonies Saturday. Police were searching the trunks of incoming cars.

Meeting with Mubarak at the vice president's heavily guarded home in Heliopolis on the outskirts of the capital, Begin was overheard, obviously referring to the assassination by asking, "How did it happen?"

A grim-faced Mubarak was heard replying, "It happened so fast, so fast."

Accompanying Begin were Israeli Defense Minister Ariel Sharon, Foreign Minister Yitzhak Shamir and Interior Minister Yosef Burg, who is Israel's chief negotiator in the Palestinian autonomy talks with Egypt.

The Israeli leadership appeared to be using the occasion to get a first-hand impression of the new Egyptian leader and to size up his intentions toward Israel.

On his arrival here, Begin issued a statement saying that the people and government of Israel had received with "great satisfaction" the news that Mubarak intended to abide by all the commitments and agreements made by Egypt under Sadat.

Later, Mubarak met with the American delegation at Tahara Palace in Heliopolis, after which Carter told reporters, "We all have confidence that Mr. Mubarak will continue the policies of president Sadat."

The former American presidents are scheduled to leave here almost immediately after the midday funeral procession and Sadat's burial.

In other developments here today, the Defense Ministry issued its first statement on the assassination by four men participating in a military parade in celebration of Egypt's greatest victory over the Israelis in the October 1973 war. It largely repeated reports from various government officials and again stressed that only four persons were involved.

But it did provide more details of the attack, identifying the leader of the assassins as 1st Lt. Khaled Ahmed Shawky Istambouly and confirming that his brother had been arrested in Sadat's massive crackdown on Islamic extremists last month.

The statement said Istambouly's brother belongs to the Takfir wa Hijra (Repentant and Holy Flight), a secret fundamentalist Islamic group, but it did not say whether the assassins were also members.

The Defense Ministry also explained that on the day of the parade, Istambouly, commander of one of the artillery units participating in the parade, granted leave to three of the regular crew manning a truck and told his supervisors they were ill. He replaced them with reservists, the statement said.

His accomplices were given the arms his original crew members possessed. Although regulations forbid anyone to have ammunition, the "traitors" managed to get their supplies from outside the armed forces and these were distributed just before the parade began, it continued.

"When the truck arrived before the main grandstand, First Lt. Khaled, who was riding near the driver, ordered him to stop and threatened to kill him if he did not. When the driver hesitated the lieutenant pulled the hand brakes, and when the truck stopped he got out," the statement said.

"The three others riding in the back followed him. At first, everybody thought the truck had stalled and they were getting out to push it. But in no time these treacherous criminals were throwing their grenades and firing into the main grandstand."

It said military intelligence was continuing its investigation and that the "general good" required that no further information be disclosed at this time.

Meanwhile, foreign dignitaries and a horde of journalists began arriving here for the funeral procession scheduled to begin Saturday at 11 a.m. (5 a.m. EDT). Among world leaders attending the ceremony are French President Francois Mitterrand, Britain's Prince Charles, West German Chancellor Helmut Schmidt, Irish President Patrick Hillery, Italian President Sandro Pertini, King Baudouin of Belgium, Chinese Vice Premier Ji Pengfei and a number of African leaders.

The only high-ranking Arab leaders so far listed as coming are Nimeri, Moroccan Prime Minister Maati Bouabid and Prince Sahar Ben Taymur of Oman.

A government spokesman said that about 1,000 media representatives are expected to be present to cover the funeral.

The government has taken extraordinary security precautions to assure the safety of the visiting dignataries and the entire area around the parade ground in Nasr City, a suburb of Cairo, where Sadat will be buried, has been closed to the public so that few Egyptians will be allowed to see their leader buried. Instead, they will have to watch it on television.

A strange atmosphere continues to prevail in this sprawliing Nile capital of 12 million people, still one more of celebration than mourning for the slain president. Like Moslems throughout the world, Egyptians are celebrating the Id Al Adha feast of sacrifice, a four-day holiday, and Sadat's death has not appeared to disturb their festivities much.

Embarrassed Egyptian officials, repeatedly asked by correspondents about the absence of public grieving, have tried to explain this by saying Egyptians are waiting for the day of the funeral to express their grief.