Egyptian President Hosni Mubarak said today that he would seek reconciliation at home with the political opposition of his slain predecessor, Anwar Sadat, while taking limited steps abroad to establish detente with the assassinated president's adversaries in the Arab world.

In a wide-ranging interview, Mubarak emphasized that he would concentrate on the pressing economic and social issues facing Egypt. He said that while "everything is going right" with Egypt's foreign policy -- particularly the peace process with Israel -- he would be looking inward, unlike his two predecessors.

"We are going to pay much more attention internally," he said, speaking English in a small reception room inside the baroque Uruba mansion, which lies across from his modest, tree-shaded home in the suburb of Heliopolis.

The interview was revealing of the new style of leadership Mubarak intends to provide his shaken country as well as of his main preoccupations 3 1/2 weeks after the dramatic assassination of Sadat at a military parade.

Quiet, seemingly confident and down-to-earth, Mubarak called the internal security situation the "main item" on his agenda, but said the Moslem fanatics involved in Sadat's killing were being rounded up and no longer represented "a big danger."

"When we arrest all these people, everything is going to settle down," he said. "You can feel people starting to be at ease as they were some time ago."

Together with several other top officials interviewed here over the past three days, Mubarak also provided some new details of the assassination on Oct. 6.

"I was looking at the aerobatics team," said Mubarak, who was sitting next to Sadat in the parade reviewing stand. "I heard some bullets, then I heard the president saying, 'impossible.' I tried to look at the president. I saw him standing up . . . I saw the image, the figure of somebody approaching with a gun, and told the president, 'Go down.'

"Somebody from behind pushed us . . . . When I fell on the ground, I felt nothing," he continued. "I fainted for a couple of seconds. Then I got up . . . I found the president with blood in his mouth. That's all that I saw."

Mubarak defended the performance of Egyptian security, which failed to intercept four assassins who jumped from a truck participating in the parade and rushed unopposed right up to the reviewing stand, firing a hail of bullets into the front row. He attributed the failure to the speed of the assassination and the security men's shock at something that had never happened in Egypt before.

"They are not used to such a violent act. It is something new in our country . . . . In your country, you are used to it, but in our country it is something we are not used to at all," he remarked.

Other officials said the military investigation, launched right after the shooting, had discovered there were eight other officers and soldiers involved in helping the four captured assassins.

One high official said they were all arrested and would be put on trial together with the four assassins. "We are satisfied that is it" inside the armed forces, he said.

Also going before a court-martial will be a "few . . . officers" who were in charge of security at the parade and allowed live ammunition to be smuggled in by the assassins, the high official said.

All 12 officers and soldiers involved in the assassination were understood to belong to a small, civilian, and fanatical Moslem group called Al Jihad. Its leader, it was learned in these interviews, was Mohammed Abdel Salam Faraq, an engineer who has worked in Cairo but was born in Beihaira, near the costal city of Alexandria.

More than 500 members of the terrorist Moslem group have been arrested so far, and more are being rounded up almost daily.

Mubarak indirectly criticized Sadat for failing to crack down sooner than he did on Moslem fundamentalist activities in the country. In early September, over 1,500 Moslem and Christian extremists, as well as political opposition figures, were detained, but Mubarak said, "We should have done this one year ago."

At another point, he said the Islamic fanatics had begun expanding their activites a long time ago, but Sadat had not wanted to take any action against them. He did not explain Sadat's reasons.

But he said he thought the Moslem extremists were no longer a serious danger, and asserted that their loss of influence within Egyptian society was reflected in the fact that fewer women were wearing traditional Moslem veils and long robes than before the assassination.

"I think you can notice it now," he said. "You can find the rate of these people women wearing veils going down very sharply, especially at the universities."

Mubarak went to great lengths during the interview to give assurances that he plans no change in Egyptian policy toward Israel after the final Israeli withdrawal from the occupied Sinai Peninsula next April 25.

Rejecting speculation that he intends to move closer, at least, to the moderate Arabs and distance himself from Israeli leaders after that date, Mubarak declared, "It will not happen.

"We have declared and president Sadat declared that our policy is not the policy of one man, but the policy of a country," he said. "After the 25th of April and we take back our territories, we will deal with Israel as any other nation.

"We will not freeze relations. Why? We are going to deal with Israel as a neighbor and like any other country anywhere in the world," Mubarak insisted. "We have rejected all means of war. So after taking back our occupied territories, why are we going to raise hell or to start any kind of bad relations?"

"I didn't even think of it," he added.

Mubarak also explained his attitude toward Arab nations that had been hostile to Sadat but had moderated their stand toward Egypt since his death, particularly Saudi Arabia.

He said he had ordered a halt to all attacks in the Egyptian state-controlled media against other Arab nations, including Libya, but that he did not intend to go further in initiating a rapprochement with them.

"We are going on the principle of wait and see," he said. "If they want to start good relations with us, we are ready, but on the basis that we are not going to drop our relations with Israel by any means. There is Camp David and we respect it," he added, referring to the U.S.-sponsored accords that brought peace between Israel and Egypt and provided for the still unfinished negotiations to settle the problem of Palestinians in occupied territories.

Mubarak said Egypt planned to go ahead with the Palestinian autonomy talks no matter how other Arab nations responded, adding, "If they accept this, they are welcome. If they don't accept this, it's their problem."

He said he would not attend the forthcoming Arab summit in Morocco, even if he were invited. He did not give any reason for this position.

The new Egyptian leader also rejected speculation that he was planning any radical shift in Egypt's alliances with the great powers. Sadat, on taking office, broke Egypt's ties with the Soviet Union and engineered an alliance with the United States.

Mubarak said there was a fundamental difference between Egypt's relations with the Soviet Union and those with the United States that explained why Sadat had expelled 17,000 Soviet technicians in 1972.

"The United States does not interfere in our internal affairs, but the Soviet Union wanted to interfere in every minor detail, in all the details of our country," he remarked.

Despite stints in the Soviet Union for training as a bomber pilot and for a 13-month course in a military academy, Mubarak said, "I am an Egyptian. I'm not a Soviet, not Polish. I'm not a European, I'm not an American. I'm an Egyptian . . . . I deal with those who respect our will and who deal with us on an equal basis."

Asked about what other steps he thought the Reagan administration might take to enhance its standing in the Arab world following the sale of AWACS radar planes to Saudi Arabia, Mubarak said, "The most important point for this area is the peace process."

Whenever Egypt, the United States and Israel reached an agreement on autonomy for the 1.2 million Palestinians living in the Israeli-occupied West Bank and Gaza Strip, Mubarak said, "I think it would be for the peace in the whole area, which will help so many things for the United States.

"We have so many dangers around us," he added, excluding Libya as one of them but refusing to say otherwise what these might be. "I don't want to name anything now."

Mubarak made it clear that he was far more preoccupied with Egypt's internal situation that with foreign policy now. He discussed the problems of birth control in a nation growing by more than 1 million people a year, of the need for increased food production to feed a population of 42 million, of the acute shortage of family dwellings and of new roads, telephone exchanges and public buildings to replace old ones badly run down.

He said he was going to open a wide public debate on all of these issues, as well as on the $3 billion in government subsidies for food, gasoline and other goods. "We will make a big discussion until we conclude something," he said, indicating he would ask the three legal opposition parties to participate.

Indicating an area where he intends to change Sadat's style of rule, Mubarak suggested he was going to keep his wife, Susan, out of the public eye, in contrast to the visible role of Jehan Sadat.

Mubarak denied reports circulating here that he is already vexed by the American media, particularly because of three recent articles by columnist Jack Anderson alleging irregularities in the way a contract was awarded to the Egyptian company transporting U.S. arms to Egypt. Among those Anderson alleged were involved in the deal was Mubarak's brother-in-law, Gen. Mounir Sabet, now stationed in Washington as chief of Egyptian military procurement, and Defense Minister Abdel Halim Abu Ghazala.

Mubarak , who reportedly was infuriated and stung by the allegations because of his reputation at home for honesty, said today that he had ordered a complete investigation of the charges here and in the United States, and had been told there was no substance to the Anderson reports.