Egyptian President Hosni Mubarak, warning that "the time factor is crucial to the success of our endeavors," urged President Reagan yesterday to use U.S. influence to achieve the withdrawal of Israeli forces from Lebanon and seek an expansion of negotiations to resolve the Arab-Israeli conflict.

"I believe that a golden opportunity exists, and it would be a grave mistake to miss it," Mubarak said following a White House meeting with Reagan and senior U.S. foreign policy officials.

U.S. and Egyptian officials agreed privately that the main reason for Mubarak's visit was his desire to convey personally to Reagan his feeling that too much time is being lost in the effort to capitalize on the peace initiative set forth by Reagan Sept. 1.

In particular, Egyptian sources said, Mubarak feels that no progress can be made toward inducing King Hussein of Jordan to join Egypt and Israel in a broadened peace process while Israeli troops continue to occupy substantial parts of Lebanon.

In addition, these sources continued, Mubarak fears that a prolonged stalemate over withdrawal from Lebanon could stall the wider peace effort to the point where it is overtaken by domestic American political factors, such as the start of the 1984 presidential campaign. Should that happen, Mubarak was said to believe, the Reagan initiative would be in danger of being put on the back burner indefinitely.

A breakthrough in the peace process would be of major importance in Egypt's efforts to regain its role as the dominant country of the Arab world--a position it lost when Anwar Sadat joined the 1978 Camp David initiative and concluded a peace treaty with Israel.

That act made Egypt a virtual outcast in the Arab world. As a result, Mubarak is eager, for reasons involving his domestic standing and Egypt's influence in the Middle East, to demonstrate that the Egyptian course of negotiation, rather than confrontation, offers the best hope of redressing Arab grievances against Israel.

When he said goodbye to the president, Mubarak made his priorities clear. He said, "Top priority must be given to reaching agreement on the withdrawal of Israeli forces from Lebanon . Upon achieving that, other aspects of the problem would be easier to solve."

Noting that he has supported the Reagan initiative, Mubarak added: "We earnestly hope that the weeks ahead will witness movement toward the negotiating table by all the parties concerned."

He said he was "encouraged" by what he has heard from Hussein and other Arab leaders about the possibility of an agreement with the Palestine Liberation Organization that will give Jordan a go-ahead to enter the talks on the future status of the Israeli-occupied West Bank and Gaza Strip.

Privately, Egyptian officials were even more explicit, saying they believe that Hussein is close to winning the backing he wants from the PLO and key Arab states and will soon announce his willingness to join the peace process. But, the officials cautioned, such progress hinges on getting a quick withdrawal of the Israelis from Lebanon.

Reagan, in his public White House remarks, assured Mubarak of his "determination to support the territorial integrity, independence and sovereignty of Lebanon" and to achieve "a comprehensive peace settlement . . . while meeting the legitimate rights of the Palestinian people."

The United States is seeking to put pressure on Israel for progress in Lebanon through such measures as making clear that it does not want Israeli Prime Minister Menachem Begin to visit Washington until a withdrawal accord is reached. But Reagan also has ruled out for now the idea of cutting off U.S. aid to Israel, and he is understood to have told Mubarak that such pressures probably would be counterproductive.

Egypt, which already is the second-largest recipient of U.S. foreign aid after Israel, also is seeking some increases in the approximately $2.2 billion it currently receives. U.S. officials, while stressing that there are strict limits to what can be done, reportedly are prepared to increase security assistance somewhat to help cover the rising costs of weaponry earmarked for the Egyptians and to offer greater help with pressing economic problems such as modernizing Egypt's water and sewage systems.