The nation's mayors were told yesterday they should be prepared to cut municipal spending as a result of California's tax-slashing Proposition 13.

The warning came from Clark Burrus, president of the Municipal Finance Officers Association and comptroller of the city of Chicago.

"All of us are going to have to be prepared to tighten our belts and operate with a reduced budget," Burrus told mayors here attending the 46th annual convention of the U.S. Conference of Mayors.

However, several local officials argued that cities generally have been fiscally prudent and that state and federal governments are to blame for their current problems and should bail them out.

The comments came at a seminar on the national implications of California's vote June 6 overwhelmingly approving the proposition to reduce local property taxes and limit state efforts to raise new taxes.

"We're always tightening our belts," said Mayor Robert J. Quirk of Cuyahoga Falls, Ohio. "I think it's time that the federal government tighten its belt."

Mayor Helen Achilles complained that in her city, San Gabriel, Calif., municipal labor leaders would not cooperate in holding down wage costs. Mayor Arnold Rue of Stockton said the people voted for Proposition 13 to "hit federal and state government, too."

But Mayor David K. Hayward of Redondo Beach, Calif replied, "We've been blaming labor and state and federal governments. We're looked to for leadership and none of it has been shown yet."

Ralph Saulnier a New Bedford, Mass., city councilman , said that while local officials are saying "don't blame us" for increased spending , they eagerly accept federal money, which is often "wasted and [WORD ILLEGIBLE] ."

"Every federal program that comes out, our city has taken advantage of it," Saulnier said. "If the plague were being passed out, we'd be the first in line."

Wayne F. Anderson, executive director of the Advisory Commission on Intergovernmental Relations, said the mayors "better not forget that the largest rising portion of the federal budget is the proportion of aid that goes to states and localities. It was $7 billion in 1960 and $80 billion in 1978."

But Syracuse Mayor Lee Alexander said part of the $80 billion is in funds such as aid to veterans that local governments "never see."

Alexander, who is this year's president of the conference, said that mayors have already responded to calls for frugality, and that for most cities' local revenues stand still but operating costs keep going up.

Anderson conceded, "The federal government has purposely raced local governments' fiscal engines" by requiring matching funds and certain taxing efforts from jurisdictions that receive federal funds.

The conference's resolutions committee adopted a call for state legislatures to study tax revision. This resolution, which will be submitted Wednesday for a vote of the 250 mayors attending the conference, charges that federal and state governments mandate local social programs without providing adequate funding, so that localities are forced to use local property taxes to finance them.