A group of mayors, governors and local officials told President Reagan yesterday that they support his "New Federalism" proposals, but each faction ticked off a list of major changes it is seeking that would radically alter the plan.

It was the first time that the 18 state, city and county leaders had met as a group to discuss Reagan's plan to transfer several federal programs to the states, and the differences among the factions were quickly evident.

Reagan mostly listened, according to several participants, but did promise to provide some federal aid directly to local governments "so they'll get their fair share."

Vermont Gov. Richard Snelling (R), for example, said Reagan should expand his plan to take over the Medicaid program by including benefits for millions of "medically needy" patients just above the poverty line.

These patients are now covered as an option by more than half the states, which might have to pay the full cost under a federal takeover or drop them from the Medicaid rolls.

Cleveland Mayor George Voinovich (R) said that federal aid for such traditionally local programs as community development grants should be given directly to cities for at least five years. He said that Ohio officials recently "skimmed" half the funds from a new federal block grant for health care, raising suspicions that states might grab a growing share of federal money intended for the cities.

William Murphy (R), executive of Rensselaer County, N.Y., said it would be difficult for county officials to support Reagan's plan unless the president promised to make no more domestic budget cuts until the recession ends. Reagan made no such commitment, according to those present, although he insisted he would not use New Federalism as a vehicle for additional cutbacks.

Detroit Mayor Coleman Young (D) said Reagan's approach should not be used as an excuse to abandon federal enforcement of constitutional rights.

Mayor Ferd Harrison (D), of Scotland Neck, N.C., said no federal program should be dropped until after an experimental testing period.

A White House aide said it was helpful to "air the differences" among the groups, each of which has been making different demands, before the president makes a firm proposal next January.

Murphy said afterward that Reagan had "gone a long way toward placating the fears of local officials." But Maine Gov. Joseph Brennan (D) said he thought the whole issue had been placed "on the back burner."