President Mubarak is manifestly trying to rebuild relations with Arab nations that were alienated by Egypt's separate peace with Israel. To do so is in the interest not only of Egypt but of a Middle East stability that depends upon reduced tensions all around. Renewed Arab ties, however, must not be bought at the expense of slackening the Camp David process with Israel - a possibility that has clouded the final Israeli withdrawal from Egypt's Sinai April 25.
The welcome climax of the Egyptian President's first trip to Washington was his pledge to pursue this process beyond the return of the Sinai. ''Irreversible'' was his word for the policy of seeking understanding and friendship with the Israeli people. Countering concerns that Cairo would take the Sinai and run, he said that the completion of the withdrawal would encourage further Egyptian-Israeli interaction and remove one more psychological barrier in the progress to full peace.
Saying it is not doing it, of course. But Mr. Mubarak evidently conveyed a sense of candor and competence in Washington, as he has at home. He not only challenges himself to follow through but challenges the other parties involved to respond in kind.
* Are his Washington hosts, for example, giving the Middle East peace process the priority attention it deserves? Secretary of State Haig's two recent trips were a step in the right direction after Camp David had seemed to fade into the background. But the failure to name a high-level US negotiator for the crucial Palestinian autonomy talks seems a step backward again. It does not inspire confidence when the administration argues that Mideast inexperience is an advantage in providing a fresh outlook for the designated man - Washington lawyer and former State Department official Richard Fairbanks. It is nothing against Mr. Fairbanks to say that he and his seniors will have to work hard to make the move successful in both imagery and substance.
* Israel is well known for its hard bargaining on Palestinian autonomy. It did not want European participation in the Sinai peacekeeping force linked to a code word like self-determination for the Palestinians. But it was responsive in the sense of accepting this participation when the nations affirmed their only condition was adherence to the Camp David accords. It ought to seize the opportunity for positive engagement with a man of Mubarak's constructive intentions.
* The Arabs might well look at President Mubarak's devotion to peace, too, and aid - or at least not obstruct - him. After all, Arabs must agree with his insistence on a form of autonomy acceptable to the ''moderate Palestinians.'' The Camp David process is the only game in town for achieving that autonomy.
Indeed, Mr. Mubarak sees the peace process eventually involving the United States and Israel in dialogue with the Palestinians, not excluding the PLO. President Reagan said he'd love to have the PLO agree to the conditions - such as recognizing Israel's right to exist - which the US has laid down for dialogue. The question for the PLO is whether it can reasonably expect to have a more effective man than Mubarak on the side of the Palestinians - and whether there might be no better time for a public acknowledgment of a fact of Mideast life, the existence of Israel. Such a gesture could nudge Camp David into the action whose continuance will require the good offices of everyone.