When mayors meeting last week with President Reagan warned that federal program cuts could lead to a rise in youth crime, his answer was cut youth wages.

Some mayors opposed the president's proposal for a lower minimum wage for teen-agers but New York Mayor Edward Koch said he thought it ought to be tried and volunteered his city as one place to experiment.

And during the weekend, another mayor who was at the White House, Thomas Bradley of Los Angeles, surprised and shocked labor supporters by saying he, too, would not object to having a pilot program test in his city. b

The mayors' discussion prompted Reagan to recall more than a half-century ago when he was a teen-ager working on a construction crew and there was no minimum wage or deductions from his pay for income taxes or Social Security. Reagan said he did not make much but the boss came out to the work site on payday and gave him his salary in cash.

Washington Mayor Marion Barry had raised the issue when he told the president that half the youth here between the ages of 18 and 25 are out of work and half the crime is being committed by persons under 20. He said he was concerned that spending cuts might exacerbate those problems.

Reagan said he not only believed that minimum wage laws were pricing youth out of the labor market but said he also did not feel it was necessary to take Social Security out of their paychecks when they did find part-time or summer jobs.

He recalled distastefully how he had to wait four hours some years back to pick up a Social Security card for his then 3-year-old daughter so she could appear with him on his General Electric television program.

Mayor Richard Hatcher of Gary, Ind., president of the U.S. Conference of Mayors, indicated opposition to the "subminimum wage" proposal, which is popular with Reagan and conservatives on Capitol Hill but opposed by labor and civil rights groups. Hatcher raised one of the standard questions asked by liberals: would it not lead employers to throw adults out of work to take advantage of the cheaper labor of youth?

Reagan said he was skeptical that would happen for summer and entry-level jobs.

Reagan urged the 12 mayors who met with him and his staff Feb. 3 to think about possible social reforms, prompting Koch to suggest that he try out the subminimum wage idea in 10 pilot cities including New York. Reagan said he would think about that.

Office of Management and Budget Director David A. Stockman had suggested in a blueprint for the president's first 100 days that proposals like the subminimum wage that antagonize organized labor be deferred to keep controversy from undermining the budget reduction operation. Stockman even suggested that the Reagan administration get informal agreement from conservatives on Capitol Hill that they would not bring up such proposals until the fall.

But that is probably not to be.

Sen. Orrin G. Hatch (R-Utah), chairman of the Senate Labor and Human Resources Committee, is eager to begin hearings on the subminimum wage and has tentatively scheduled them to begin in late March, an aide said.

"The senator feels no compulsion to wait for the administration to come out with a proposal on that and certainly it's a topic for which there's so much data needed we've got to start studying the thing now," the aide said.