Governors and state legislative leaders agreed yesterday to start serious negotiations on President Reagan's proposal to turn dozens of domestic programs over to the states, but warned the administration they will fight his efforts to cut federal support for those programs in the 1983 budget.

Rejecting arguments that the Reagan federalism initiative should be shelved until the economy has revived and state and federal budgets are in better shape, the National Conference of State Legislatures and the National Governors Association agreed to draft responses to the Reagan plan.

The dual decision was at least a short-term victory for the White House, which looked to the states for critical support needed to turn Reagan's proposal into draft legislation in the next six weeks. On Saturday, congressional Democratic leaders said the recession made this the wrong time for such an initiative, and some state House Democrats agreed.

But in a Capitol Hill hotel, the executive committee of the legislators' group praised Reagan for taking the "bold step" of proposing to shift control of some 40 social programs to the states. The legislators, however, made it clear that they had many problems with the details of Reagan's initiative and urged a full federal takeover of welfare and rejection of his plan for the states to run the food-stamp program.

At a hotel across the street, the governors agreed to draft what their chairman, Vermont Gov. Richard A. Snelling (R) called a "substantive" response to the Reagan offer before their meeting ends Tuesday. The governors are to see Reagan at the White House this afternoon.

Snelling and Utah Gov. Scott Matheson (D), the chairman-elect, said the governors had decided to separate the federalism issue from arguments about the size of the defense budget or the wisdom of Reagan's tax cuts.

But they said they could not accept the plea they heard from Office of Management and Budget Director David A. Stockman and Reagan's assistant for inter-governmental relations, Richard S. Williamson, to divorce federalism from the 1983 budget fight.

Snelling said the governors would oppose the $10 billion cuts in federal aid programs Reagan is seeking, and Matheson said that unless those cuts are killed in Congress, the federalism initiative is dead. "We can't take another hemorrhaging like we had last year," he said.

The two groups acted after Stockman and Williamson had made it clear that Reagan is ready to consider general revenue financing of the transition trust fund to support programs returned to the states. They also said that he would guarantee that no state would have its federal aid reduced during the transition period from the fiscal 1983 level Congress sets--even if that is higher than his own budget proposal.

The two officials also said Reagan was "open to discussion" on the details of his proposed swap and turnback program.

Reagan has suggested that the federal government take over full funding of Medicaid, while the states take food stamps and the federal share of Aid to Families with Dependent Children.

Among the governors, considerable interest was shown in alternatives drafted by Matheson and Georgia Gov. George Busbee (D). Matheson would have the federal government take over Medicaid and keep food stamps and AFDC, at least for now, with the states using their Medicaid savings to finance a negotiated list of federal programs.

Busbee would also keep food stamps in federal hands, but would have the states take over AFDC and Medicaid payments for AFDC recipients. The federal government, in turn, would assume the state share of Medicaid for the aged, blind and disabled.

The biggest concession made by the administration today was on the financing of the trust fund that would handle the four-year transition of some 40 domestic programs from federal to state control. Originally, Reagan suggested it be financed by about $11 billion of federal excise taxes and $17 billion from the oil windfall profits tax.

States complained that the windfall tax would expire by 1991 and leave them holding the bag. Stockman and Williamson repeatedly said Reagan was ready to consider "other alternatives" on that, mentioning specifically and favorably a proposal by Sen. David F. Durenberger (R-Minn.) that would use federal income tax revenues, instead of the windfall profits taxes, for the fund.

The legislators' resolution praising Reagan came after heavy lobbying by White House aides. They were able to pick up support from southern Democrats while holding Republican legislators solidly in line behind the resolution that gave qualified support to the administration's federalism initiative.

A Democrat, Richard S. Hodes, the majority leader of the Florida House, sponsored the resolution. He made it clear he was doing so even though he had some strong reservations.

Industrial state Democratic legislators had tried to tie the federalism issue to the controversy over the Reagan cuts.

"There's crystal disaster facing all of us down the road," said New York Assemblyman William F. Passannante (D). He urged unsuccessfully that they call for reductions in military spending, a restructuring of the administration's corporate tax program and an end to cuts in domestic programs.

But, clearly, the $10 billion in cuts in federal aid to state and local governments were of concern to both Republicans and Democrats. NCSL President Ross Doyen, the Republican president of the Kansas Senate, had joined with Passannante in a statement released earlier this month, saying the legislators could not accept the new cuts Reagan proposed because they would have an "adverse effect on our ability to cope with citizen needs."

Yesterday, South Carolina Gov. Richard W. Riley (D) told Stockman that unless Reagan curbs federal deficits, he is just offering the states "borrowed dollars to meet real responsibilities."

When Stockman replied that "if we make the federalism initiative hostage to a balanced budget, we will have a long wait coming," New Hampshire Gov. Hugh Gallen (D) accused him of "changing the philosophy of your party" that deficits are dangerous.