President Reagan, welcoming Egyptian President Hosni Mubarak to the White House, said yesterday the Palestinian problem should not be allowed to "fester" any longer and called for "practical, not merely rhetorical, steps" to restart the stalemated peace process.

As both presidents stressed the "vital role" of the other's nation in reviving the peace process, sources said here that U.S. and Egyptian officials are discussing new ways to begin negotiations on local autonomy for the Israeli-occupied West Bank and Gaza Strip as a step toward a peace settlement.

A senior administration official, briefing reporters on the hour-long meeting, said Reagan and Mubarak engaged in "a very animated" and "very frank" discussion of difficulties in reviving the peace process. He warned against expecting an announcement of any new initiative at the end of Mubarak's visit here Friday.

"You're not going to find in this a breakthrough event," he said. "We are still cumulating our thoughts on this."

"We agreed that we both are interested in remaining flexible on devising ways to move," he said, adding that any movement had to be on "both procedure and substance," following consultations with Israel and Jordan.

{At a White House state dinner last night, Mubarak condemned Israel's policy of "shooting and beating in a land that is holy to us all." Although he did not mention Israel by name, he said, "no one in good conscience can condone" a policy of violence against Palestinians in the West Bank and Gaza Strip, staff writers Donnie Radcliffe and Jacqueline Trescott reported.}

Reagan and Mubarak also discussed the Iran-Iraq war earlier yesterday, according to the senior U.S. official. He said Mubarak, who recently toured Arab states on the Persian Gulf, had relayed "the concerns of the region" that "there is going to be an American withdrawal, decreased naval presence" in the gulf.

Reagan told Mubarak, "We are not withdrawing," the official said. But Reagan warned that "there may be changes in our naval configuration" and a "rationalization" in the fleet of 28 ships now convoying U.S.-flagged Kuwaiti tankers.

The administration official refused to specify what Reagan and Mubarak discussed as possible new "practical steps" to revive the Mideast peace process. But he made it clear they had spent little time on five of Mubarak's proposals, including a six-month halt to violence and to new Israeli settlement activities in the occupied territories.

"These have not been discussed in detail with us," the senior official said.

To Mubarak's call for a halt to violence in the territories for six months, the official said the United States responded favorably. "We said that's sensible," the official said.

The failure of the two presidents to discuss specific items fueled speculation that the United States and Egypt are attempting to devise a new formula for reviving peace talks.

Significantly, the U.S. official also said the two sides had not discussed the participation of the Palestine Liberation Organization (PLO) in an international peace conference. Mubarak's efforts to press the Reagan administration to begin talks with the PLO during his last visit here in September 1985 met an icy reception.

U.S. officials believe the main block to relaunching peace talks is Israeli Prime Minister Yitzhak Shamir, who has systematically refused to consider any approach other than that provided in the 1978 Camp David accords.

The accords were supposed to lead to talks on "transitional arrangements" to provide "full autonomy" for an initial five-year period on the West Bank and Gaza Strip as a step toward a peace settlement. Under those arrangements, Israeli military and civilian authorities were to withdraw once Palestinian inhabitants elected their own "self-governing authority."

Those talks were never held, and the PLO and all Arab countries except Egypt rejected the accords outright. Now, however, implementation of those elements of the Camp David accords is being discussed as a means of lessening tension in the occupied territories, according to U.S., Israeli and Egyptian sources.

The PLO has authorized Palestinian leaders from the West Bank and Gaza Strip to enter discussions with Israeli authorities on "interim arrangements," Hassan Rahman, the PLO representative here, said.