Eleven Democratic big-city mayors, meeting yesterday at the home of New York Mayor Edward Koch, drew up a $16 billion proposal for economic aid to cities, and said they would seek to present the plan immediately to President Carter and congressional leaders.

The plan puts dollar figures on a general economic stimulus resolution passed earlier this month at the U.S. Conference of Mayors' annual meeting in Seattle.

In an appearance at that meeting, Carter emphasized his determination to stick to a policy of fiscal restraint and to resist increases in domestic spending.

But the mayors, who endorsed Carter for reelection at the Seattle conference, apparently feel that they have some leverage now and hope to translate their political support into additional federal money for their financially strapped cities.

While the mayors were careful to state their continuing support for the president, several indicated if nothing were done" to respond to their cities' needs, one participant in the meeting said.

The mayors, concerned over a deepening recession that has thrown thousands of residents of industrial cities out of work and cut into tax revenues, have asked for $1.25 billion in antirecession aid -- $1 billion tied to the national unemployment rate and $250 million tied to local unemployment rates. That proposal is not new, but legislation authorizing the aid is languishing in conference committee on Capitol Hill.

The largest single item in the mayors' new plan is a $4 billion request to fund energy conservation, including weatherization. The mayors also will ask for $1 billion in "energy conservation block grants," similar to the popular community development block grants, through which cities can fund programs especially tailored to their needs.

Meanwhile, the Carter administration has announced a $71 million program to help rebuild riot-torn areas of Miami, whose mayor, Maurice Ferre, was among those attending the New York meeting.

The announcement came just a week before Carter is to appear at an NAACP convention in Miami. His last visit to the area, shortly after the mid-May riots that killed 18 and destroyed $100 million in property, was marred by angry crowds hurling rocks at his motorcade.

Carter is to address the convention Friday, the Fourth of July. Independent candidate Rep. John B. Anderson (R-Ill.) is to speak Tuesday, and Carter's challenger, Sen. Edward M. Kennedy (D-Mass.), is to speak Wednesday.

Mayors attending the meeting in New York, besides Koch and Ferre, were Lee Alexander of Syracuse, Ernest Morial of New Orleans, Richard Hatcher of Gary, Ind., Jim Conway of St. Louis, Charles Royer of Seattle, Dan Whitehurst of Fresno, Calif., Doug DeGood of Toledo, Ken Gibson of Newark, N.J., and Henry Maier of Milwaukee.