Governors and mayors often fight over money. This year, with taxpayers in revolt, the struggle is even more intense.

Yesterday, after mayors attacked them for two days in a row, the governors fired a salvo of their own: a blunt suggestion that mayors themselves ought to do more to curb spending.

The verbal jousting took place as the National Governors' Association began its 70th annual conference here to discuss a wide range of issues including national health insurance, welfare revision, crime, economic development and urban aid.

Before the governors could get their three-day show started, the National Conference of Democratic Mayors, led by Kevin H. White of Boston, charged that the governors were not dealing seriously with tax revision. White also accused Massachusetts Gov. Michael S. Dukakis of not doing enough for this city.

Dukakis replied sharply yesterday on ABC's "Issues and Answers" that there should be "fewer speeches from city hall and more efforts to control city spending."

The governor, who has campaigned nationally for more state aid to localities, said he was "a little puzzled" by White's remarks since Massachusetts has just approved move than $300 million in new funds for cities and one-fifth of the money is going to Boston, which he said "has only 10 percent of the state's population."

Gov. William G. Milliken of Michigan, chairman of the association, said states are sharing much more of their revenues with localities - $73 billion this year, twice what they were sharing 12 years ago.

Voters in several states have demanded referendums in November on measures to cut spending or revenues or both in the wake of California's vote in June to slash property taxes and limit future tax increases.

Governors here are sensitive to reports of huge state surpluses and are quick to insist that they don't have California's $5 billion extra. Other states, they say, have an aggregate surplus of $6 billion, not the $30 billion that some members of Congress have alleged.

Four governors, asked on the ABC telecast to rate President Carter, spilt along party lines.

Dukakis, a Democrat, praised the president for consulting often with governors. He said he was disappointed over Carter's failure to get his energy program enacted but added: "He's been pushing and Congress hasn't been responding."

Gov. James B. Hunt of North Carolina, also a Democrat, said Carter is doing a "good job" and predicted he will "come back in the polls."

Milliken, a Republican, said Carter had promised more than he has been able to deliver. But on the energy impasse, Milliken said, "the president cannot be totally faulted for that." He said it was "unconscionable" that Congress has not acted on the program.

Gov. Robert D. Ray of Iowa, a Republican, criticized Carter for allowing more beef to be imported, which he said has hurt domestic livestock farmers.

Milliken and Dukakis were asked about the political influence of governors this year in view of the administration's proposals to leave states out of its $1 billion supplemental fiscal aid program and to bypass states in sending anticrime aid to metropolitan areas. The Senate Finance Committee has put states back into the fiscal aid program, and of the anticrime funds Milliken predicted, "We'll win that battle."

Governors of both parties pressed presidential assistant Jack H. Watson Jr. for the administration's position on including states in renewal of the general revenue-sharing program, which will come before Congress next year.

Carter, who said during the 1976 election campaign that states should be dropped from this program, has made no decision, Watson said. But it was clear that the governors expect to find themselves opposed to the White House on this issue as well.

However, there were indications that the governors will support Carter's battle to overhaul the federal civil service, and Watson brought a personal appeal from the president for help in the House vote expected in early September.

The association's executive committee recommended approval of the constitutional amendment giving the District of Columbia voting representation in Congress.

Ray, continuing a GOP effort to be identified with the amendment, said "People may ask why a governor from why out in Iowa is introducing a resolution for the people in Washington, D. C. My only answer is: 'Why not?'"