A group of big-city Democratic mayors wary of a political confrontation with the White House, but worried that the administration is retreating from its early promises for a new approach to urban problems, is seeking ways to increase its leverage in Washington.

"We support Jimmy Carter, but we represent a constituency that can't wait very much longer," said Gary, Ind., Mayor Richard Hatcher, president of the National Conference of Democratic Mayors which has been meeting here two days.

Hatcher called this strategy session - the first of its kind - because the State of the Union message and the federal budget which goes to Congress next week will give new indications what intentions Carter has for the cities.

"We've been able to persuade them that it's necessary to have an urban policy," Hatcher said, "but there's a gulf between that and what's necessary from our point of view."

But the mayors are uncomfortable criticizing a President of their party in public and remember the sharp words Carter had in July for National Urban League President Vernon Jordan when he criticized Carter for failing to follow through on campaign commitments to blacks.

With only seven weeks remaining before Carter's promised delivery of his urban policy, the mayors all said their relations with Washington are better than during the Ford and Nixon administrations and they hope that Carter's early pledge of a new urban approach will be redeemed.

But, they are also groping for a way to make themselves heard better. This session format is an attempt. Previously, mayors caucused during gatherings of the U.S. Conference of Mayors or the National League of Cities.

Although mayors disagree how best to approach Washington, they are united in opposition to a major part of Carter's domestic program, the tax cut of a reported $25 billion.

From their perspective, reduced federal taxes mean higher local taxes.

"I'm baffled by these economics," said Mayor Henry Maier of Milwaukee. "Local officials can't give tax cuts, we've got to raise taxes."

Maier, Hatcher and Mayors Frank Logue of New Haven, Conn., and Daniel Whitehurst of Fresno, Calif., expressed unhappiness with any tax reduction that is not accompanied by tax incentives for businesses in central cities.

"There's not a mayor alive who can tell a businessman thinking of leaving his city take your 1,500 jobs and stick them in your ear," Logue said. But he pointed out that the mayor can't take businesses an attractive offer to meet competition from non-urban areas of the Sunbelt.

Only the federal government can help in those cases, said Logue.

A delegation representing the Democratic mayors will seek a meeting with Carter to explain the concern. "We're trying to get in before the policy is made," Mayor Lew Alexander of Syracuse, N.Y., said.

But the mayors are painfully aware that their image is tarnished in Washington and elsewhere. "So often we're perceived as people just seeking money," Alexander said, "but we want not only money but better use of federal power."

In Hatcher's words, a federal urban policy should be "a blueprint for turning the cities around" and not just present federal programs with a little sweetener added.

"The question," Hatcher said, "is whether the cities are seen as important enough for that kind of new commitment."