Forming a fragile "united front," leaders of the five major groups representing state and local government officials yesterday urged President Reagan to exercise "restraint" in cutting domestic social programs and requested that he convene early in January a "domestic summit" with them and congressional leaders.

The statement came amid indications that pressure from mayors, governors and some Republican leaders in the Senate had already moved the White House to reconsider some of the deep cuts in job training and other social programs recommended by the Office of Management and Budget.

Reagan, who previously had stressed to local officials that they would have to endure some pain in the next round of budget cuts, made a point of telling a group of governors and local officials at the White House on Tuesday, "I do not intend to balance the budget on the backs of cities and states."

In their statement yesterday, the state and local groups suggested that future cutbacks in spending ought to focus on federal entitlement programs and that "rigorous efficiency and equity reviews should be applied" to the military budget.

"Those who through no fault of their own--the children, the poverty-stricken, the disabled, the elderly, all those with true need . . . should be assured that the programs they depend on are exempt from federal cuts," the statement said.

Endorsing the statement were representatives of the National Governors' Association, the National League of Cities, the U.S. Conference of Mayors, the National Conference of State Legislatures and the National Association of Counties. It was their first joint meeting since June, 1980, and it represented something of a truce in the feuding between mayors and governors over money and power that characterized the skirmishing over the cuts Reagan got approved by Congress last summer.

The governors had been strongly in the president's corner then, because he had promised them more power over programs in exchange for funding cutbacks. But when the dust settled, the governors said they felt the cuts had been deeper than they could live with, and they had gotten in return little in the way of new authority. Their current president, Vermont Gov. Richard A. Snelling, a Republican, was the catalyst for the meeting yesterday.

"Our highest priority is to fight, if need we must, for adequate funding to assure that we meet our obligations," Snelling said yesterday. "In the past, there have been some at the federal level who have been advantaged by our disunity."

Snelling and the mayors' groups have called for a moratorium during the next three years on cuts in aid to states and cities, but representatives of state legislators and county officials would not agree to that language in the statement yesterday, saying it sounded too negative.

In recent days, Sen. Paul Laxalt (R-Nev.), the president's closest friend in the Senate, Majority Leader Howard H. Baker Jr. (R-Tenn.) and Budget Committee Chairman Pete V. Domenici (R-N.M.) have suggested that contemplated cuts in domestic programs were excessive.

There were indications yesterday that the White House was seriously studying a Domenici proposal for keeping the affected programs at their current dollar levels in the next three years and instead curbing the growth in various entitlement programs.