Washington — Egypt's President Hosni Mubarak has reaffirmed his nation's commitment to peace with Israel. But barring an Israeli commitment to withdrawal from Lebanon and progress on the Palestinian issue, it will probably continue to be what one Egyptian official calls a ''cold peace.''
Some Middle East specialists fear that unless the Reagan administration can bring about progress on these two fronts, Egypt will move, slowly and discreetly , in the direction of nonalignment.
In his meeting on Thursday with President Reagan, President Mubarak seemed to be carrying two messages:
* The United States must show progress toward securing an Israeli withdrawal from Lebanon, or President Reagan's Middle East peace plan will soon lose credibility among the Arabs.
* The US ought to start treating Egypt as an equal to Israel when it comes to military and economic aid.
Egypt and Israel are the largest recipients of American aid. But Israel, with a population of 3 million, has stayed ahead of Egypt, with its population of some 41 million.
Given pro-Israeli sentiments in the US Congress, Egypt is never likely to get more aid than Israel, congressional specialists say. Aid to Israel for the current fiscal year is supposed to total $2.4 billion. For Egypt, it is set at about $2.3 billion.
Mubarak has been asking for more flexibility in the use of American economic aid. The Egyptians say too many strings are attached. They contend Israel gets virtually a blank check. But the administration is moving to accommodate Mubarak on the issue of flexibility.
In an interview with the Washington Post on Wednesday, Michael P. W. Stone, the new US aid director in Cairo, outlined a plan to reform the aid program. Mr. Stone wants to reduce small projects and give top priority to a few major investments. Such assistance would give more tangible evidence than has most of the aid so far that the program benefits ordinary Egyptians.
Egyptian ties with the United States remain strong. But since taking power in 1981, Mubarak has brought a cooler tone to the relationship. He has worked hard to reestablish ties with other Arab nations and has reemphasized Egypt's role in the nonaligned movement.
Mubarak now seems to be putting President Reagan to the test. The Egyptians suspect that Israel is dragging out its talks with Lebanon partly in order to divert attention away from the Reagan peace plan and possible negotiations over the Israeli occupation of the West Bank of the Jordan River. As one Egyptian diplomat put it, the Egyptians will consider an Israeli commitment to withdraw from Lebanon as ''proof of the US ability to deliver.''
''If the US can't get a commitment from the Israelis to withdraw from Lebanon , what will it do when it comes to the West Bank?'' the diplomat asked.
The Egyptians fear that if Reagan cannot produce results by this summer, Middle East issues will become entangled in the American presidential election campaign and diminish Reagan's ability to put pressure on Israel.
William B. Quandt, a leading Middle East expert in the the Carter administration, says that if there is no progress on Lebanon and on the Palestinian issue, President Mubarak ''is going to have to move more toward nonalignment.''
Quandt says the stalemate over Lebanon and the West Bank has increased pressure on Mubarak from three sectors inside Egypt: Islamic fundamentalists; traditional leftist opposition; and professional Egyptian diplomats who have become disillusioned with the Egypt-Israel peace treaty.
But Joseph J. Sisco, a former top US negotiator in the Middle East, says Egypt and the United States have so many mutual interests that no fundamental realignment by the Egyptians is a prospect.
Although Mr. Sisco foresees ''no quick and easy fix'' in Lebanon, he does say he believes that there will be an agreement on a withdrawal from Lebanon by both Israel and Syria within the next few months. For one thing, says Sisco, the Israeli occupation of southern Lebanon is becoming increasingly unpopular in Israel itself.