Despite reassuring pledges of continuity with the policies of his slain predecessor, Hosni Mubarak remains a largely unknown quantity whose sudden ascent to the leadership of Egypt raises troubling questions for the massive U.S. strategic investment here and about the future of Egypt's relations with Israel.

Mubarak has labored for a dozen years in the shadow of Anwar Sadat, faithfully and almost always silently carrying out policies decided by the assassinated president. Now that the decisions will be Mubarak's own, diplomats and ordinary Egyptians are wondering what they will be.

"We have seen him a lot," said a Cairo businessman, "but we don't know who he is or what he will do."

Although he has unflaggingly worked to advance Sadat's Camp David policies, Mubarak himself has never become strongly identified with them. Some reports -- vehemently denied -- have suggested he disagreed with Sadat on some issues. Observers here pointed out that he paid only one official visit to Israel, and that was to accompany Sadat to Beersheba in the Negev.

Mubarak's chief foreign policy adviser is said to be Osama al-Baz, a high Foreign Ministry official who repeatedly has urged Sadat to take tougher stands in dealings with Prime Minister Menachem Begin of Israel.

Mubarak also remains an enigma to Israeli leaders, who have been shuttling to Cairo over the last four years but have had little contact with Mubarak, Washington Post correspondent William Claiborne reported from Jerusalem. In an exception to that lack of association with Israelis, however, Israeli sources said Israel's first ambassador to Cairo, Eliahu Ben-Elissar, now a member of parliament, saw Mubarak often and established a kind of rapport, Claiborne reported.

The question of what Mubarak has in mind is particularly important in a country where one-man rule is a long tradition, followed with gusto by the late president with Mubarak at his side. The questions also seem unusually pertinent to Americans, with Washington backing Egypt with the largest economic aid program in the world and a $3.5 billion military assistance package that makes Egypt a major strategic ally in the Middle East.

Mubarak has gone out of his way to reassure the United States, Israel and the world that Egyptian policies will continue on the course set by Sadat in the framework of the Camp David peace accords.

Mubarak, in a symbolic gesture to underscore his commitment to the peace process, today granted his first interview as president-designate to a Jerusalem newspaper, Maariv, putting the Israeli request ahead of hundreds of others from the local and world press.

In another interview, with CBS' Walter Cronkite, Mubarak said tonight, "We are committed to what we have signed," and answered, "Why not?" when asked whether his cooperation with Prime Minister Begin would be as fruitful as under Sadat.

But the assassination of Sadat appears to have originated, at least remotely, in a groundswell of Islamic extremism, whose main object of virulent opposition was the slain president's opening of Egypt to the West, particularly to the United States, and his peacemaking with Israel.

Pledges of continuity notwithstanding, Mubarak could find it to his advantage to back away from Washington and slow down normalization with Israel to blunt the appeal of the Moslem fundamentalists.

As Mubarak moves toward the presidency, most Egyptians and diplomats have gained the impression that he is firmly in charge at least for now.

Egyptian sources said that when it became known at midafternoon Tuesday that Sadat had died from his wounds, Mubarak emerged from the Maadi military Hospital on the banks of the Nile and immediately spit out a series of orders to the country's military and civilian leaders. His attitude -- and the response he elicited -- left no doubt about who was running Egypt, the sources said.

The Egyptian people also seemed to find it natural for Mubarak to appear on television to announce Sadat's death. The slain president had long groomed him to take over, keeping Mubarak's square, smiling face at his side during most public appearances.

As vice president, Mubarak earned a reputation as a strong advocate of firm security measures and a close friend of Egyptian security and military commanders. As a result, diplomats speculated that he would renew emphasis on political restrictions here, particularly in light of reports linking the assassination to elements inside the Army and to last month's religious agitation.

One key lies in an investigation going on to determine the size of the conspiracy that led to Sadat's assassination. Mubarak last night called it "a long story," but declined to reveal anything of what military investigators have discovered so far.

Discovery of a broad-based dissident movement in the Army, it is believed, would be likely to inspire Mubarak to increased caution and more attention to Islamic and Arab sensitivities as the new president seeks to take hold and build up support among the Egyptian people.

Diplomats stressed that whatever they say about the future must remain speculation because Mubarak has been too deeply in Sadat's shadow to cast one of his own. Only now, in the spotlight, will his own ideas about where to lead Egypt become clear.