A group of governors, mayors and other local officials met with President Carter yesterday to tell him, as they have told him before, they need more federal money and less federal interference in their affairs.

Calling itself "The New Coalition," the bipartisan lobbyists said the funds should come in two basic forms:

A continuation of the $6.9 billion-a-year, no-strings attached, federal general revenue-sharing program. Some in Congress and the administration would like to see the program reduced, modified in terms of distribution, or eliminated at the end of fiscal 1980.

Increased federal aid -- as much as $800 million, one coalition member suggested -- for lower-income families who will have to pay higher home heating bills this winter.

The state and local officials reminded the administration that they are perfectly capable of meeting deadlines and making site and permit decisions involved in the construction of "priority energy projects" in their states and counties.

The president's plan to establish an "energy mobilization board" that would be empowered to preempt local site and permit authority in the interest of speed and efficiency in energy project construction is not a good idea, the officials said.

"We . . . recognize the need for the federal government to establish procedures to expedite the federal approval process for priority energy projects," they said in a joint letter. But, they added, "We will be working with your administration and the Congress to insure that state and local governments will retain authority to set their own decision deadlines and to make site and permit decisions without danger of federal preemption."

Carter told the bipartisan assemblage that this intentions in suggesting the energy mobilization board were "not to subvert state and local government laws".

"The mobilization board is designed to cut through red tape and delay," he said at the beginning of the 90-minute meeting, only several minutes of which was open to the press.

"We did not resolve the energy crisis," said Gov. Bill Milliken of Michigan, a Republican who emerged from the session about 10 minutes before it ended.

"We talked briefly about welfare reform and about revenue sharing," Milliken said. He said the conferees didn't solve these problems, either.

Asked if he thought Carter's power to act on the coalition's requests was diminished by his low standing in the polls and the emergence of a possible presidential bid by Sen. Edward M. Kennedy (D-Mass.). Milliken said: "I don't think so."

He smiled, "Maybe, here in Washington, you attach greater importance to political maneuvering than we do elsewhere around the country," Milliken said.

No one discussed politics or Kennedy at the meeting. "It would have opened a can of worms that nobody wanted . . . Besides, this was a bipartisan meeting and you don't discuss politics at bipartisan meetings," one Midwest mayor said.

However, Democratic members of The New Coalition did hold informal political discussions with White House staffers before the meeting began, according to several reliable Democratic sources.

"They were talking in the hallways," one source said. "They, and I mean some governors and mayors, were telling the White House Staffers that they didn't think Carter could win in their states.

"But they [coalition members] also said they didn't think Carter would bow out without a fight, that he would graciously throw in the towel. They said they believe that there is going to be a hell of a lot of bloodletting if it comes down between Carter and Kennedy and that the party couldn't stand that," the source said.

However, Gov. Ella T. Grasso of Connecticut, a Democrat, gave Carter strong, on-the-record support:

"I support the president for renomination and have urged him to run . . . I made my commitment to the president and I intend to fulfill my commitment," she said.

Most of the 30 officials who met with Carter agreed with Milliken that the session produced nothing concrete.

The revenue-sharing program is safe for this year, but the president gave no strong indication that he will work to see it reenacted when it expires Sept. 30, 1980, the conferees said.

The administration expects a windfall profits tax on deregulated domestic oil prices to generate $400 million to help the needy meet fuel costs. But Congress has yet to pass such a tax. And at least $800 million is needed said Gov. Julian Carroll of Kentucky, a Democrat.

In summary: "It was a positive meeting. But the answers were predictable," said a spokesman for the National Governors Association.