President Reagan's free-market answer to the decay of American inner cities--urban enterprise zones that would lure new businesses to blighted areas--has underwhelmed many of the nation's big-city mayors.

Enterprise zones are the one major initiative Reagan has offered to help troubled cities, but they have drawn only passing interest from mayors struggling to arrest the economic stagnation of their cities.

"I'd rather have them than not, but I have no confidence they are going to do very much," said Minneapolis Mayor Donald M. Fraser in a view echoed by both Democrats and Republicans attending the annual meeting of the U.S. Conference of Mayors here.

Describing it as "an experimental, free-market initiative," Reagan has sent Congress legislation to create 25 enterprise zones a year in which federal taxes and regulations, as well as those at the local level, would be eased to attract business investment in depressed areas.

But when Housing and Urban Development Secretary Samuel R. Pierce Jr. told the mayors this week that enterprise zones were the administration's "top priority," he was greeted with tepid applause, and most of the mayors sat in silence.

The enterprise zones are "no miracle cure," Pierce acknowledged, but they can become "a major tool" for rebuilding the cities.

Several mayors said it was a tool they are already using. William H. Hudnut III of Indianapolis, a Republican, noted that cities have tried for many years to attract new business investment by providing tax breaks and floating industrial revenue bonds. "I think of the entire city as an enterprise zone," he said.

Added Mayor William T. McLaughlin of Wilmington, Del.: "There's nothing enterprise zones can offer that we're not doing already."

Mayor Paul R. Leonard of Dayton, Ohio, a Democrat, said there is "still some suspicion as to whether there is any validity" to the idea that tax breaks will spur inner-city business, particularly in the current economic climate. "There's no sense in debating enterprise zones until you get the economy going," he said.

The mayors' ambivalence toward enterprise zones reflects a belief that the zones alone are not enough to staunch the stagnation of cities.

"It doesn't do anything to stop the flow of wealth to the suburbs and repair the infrastructure" like deteriorating roads and sewers, Hudnut said.

Detroit Mayor Coleman A. Young said the administration wouldn't do much for the cities with enterprise zones alone. "The biggest weakness of this administration is that it has no policy to solve the problems of the cities, and seems to be saying it has no responsibility to solve them."

Young becomes president of the mayors' group this week, 50 years after it was started in the depths of the Great Depression as mayors turned to Washington in 1932 for public works jobs.

Today, however, the mayors are expecting less from Washington as the federal aid spigot begins to tighten.

"Realism is setting in--a realization that the federal government can't do it anymore. We had become addicts to federal aid, and now we're going cold turkey," Leonard said.

While the mayors had often protested Reagan's proposed cuts in domestic programs, Hudnut said, "There is a mood of resignation" among them this year.

The mayors have talked with increasing interest of turning to the private sector to pick up where the federal government left off, and enterprise zones are one of several ways they could check urban decay in place of federal aid.

But, Hudnut cautioned, "It is a mistake to assume the private sector can be the surrogate for the public sector." Noting that 70 percent of U.S. corporations made no contributions to charities last year, Hudnut concluded: "They're never going to fill the shortfall."