he National League of Cities today asked President Reagan to spare local governments from further cuts in federal aid and requested that he meet with mayors, governors and other state and local officials at a "domestic summit" before deciding on spending reductions in next year's budget.

"They're saying 'Whoa, slow down, don't pull the rug out from under us,' " explained outgoing league president William Hudnut, Republican mayor of Indianapolis. "We've taken our share of the cuts."

Federal cutbacks and the fear of more of them were the dominant topics of this year's annual meeting of mayors and council members from big cities and small towns across America, many of whom are already laying off workers, reducing services and raising taxes to cope with reductions approved by Congress last summer.

Reports from Washington that the Office of Management and Budget was considering phasing out two popular urban revitalization programs sent tremors through workshops and meetings here.

Before concluding today, the league adopted by nearly unanimous voice vote a resolution that described as "unacceptable" the proposals to phase out the Urban Development Action Grant and Community Development Block Grant programs.

"I would think there has been an escalation of concern, coupled with an erosion of support for the president's program, that the cuts are not fair and too much of a burden on the cities," Hudnut said.

While big city Democratic mayors sat back and watched, the opposition to the Reagan economic recovery program was expressed here in cutting rhetoric by Republican speakers who included Gov. Richard A. Snelling of Vermont, Mayor George Voinovich of Cleveland and Sens. Mark O. Hatfield (Ore.) and David F. Durenberger (Minn.).

Snelling called White House policy an "economic Bay of Pigs" and Voinovich said Reagan administration budget cutters were using a "meat-ax."

Durenberger pointedly told members of the league in a speech this morning that they should say: "No more, Mr. President, until you show us an income security policy that is fiscally secure, until you articulate a defense policy that is something other than an arbitrary commitment to spending increases, until the federal partner can give us an economic policy that promises stable growth, and until you give us a vision of the federal role in the federal system, it's hard to ask us to be a part of the new federalism."

Many of them were also critical of Reagan for comments he made in an interview last week in which he said he believed that the national government had no responsibility to redistribute resources between rich and poor states because a citizen always had the right "to vote with his feet."

"That is a new classic in large misunderstanding expressed in small words," Durenberger said.

U.S. Trade Representative William E. Brock was the only member of the Cabinet to attend the sessions here although the league invited Vice President Bush and five other Cabinet members.

After turning the invitations down, the White House did invite the league's state directors, a group believed to be somewhat more supportive of Reagan, to Washington for a meeting Thursday. Hudnut was not included.

It was Snelling who came up with the idea for a domestic summit for budget issues and in so doing he urged that cities and states put aside their historic power feuds, which league leaders seem to find instantly attractive.

"If they can go to Cancun and Ottawa, they can go to Kokomo and Indianapolis," the tall, silver-haired Hudnut said sardonically.

But if the president does not agree to a summit, Hudnut said, they would probably hold it anyway without him.

"I'll tell you, we'll lobby the Congress, too. The president proposes but the Congress disposes," he said with mild pique. "We feel strongly about these things."