President Reagan yesterday accepted a counterproposal from the nation's governors as the basis for negotiating draft legislation that would have the federal government assume the full costs of Medicaid while the states take over a host of smaller federal programs.

At a White House meeting, Reagan heard the governors' offer and, according to Vermont Gov. Richard A. Snelling (R), said "the proposal we put before him was an appropriate starting point" for negotiations.

Snelling, the chairman of the National Governors' Association, said that if the position hammered out by the governors just hours before they met the president is formally adopted as association policy today, negotiations with the administration will start Wednesday.

The governors' statement said the process could lead to "a revolutionary restructuring of our federal system," but Reagan indicated he would accept even "a small step" this year in that direction.

The goal is to have a bill ready for Congress by April 1, but presidential assistant Richard S. Williamson told the governors the best that can be hoped for in 1982 is Senate passage.

To the surprise of some governors, Reagan made no objection to their suggestion that the future of the food stamp and Aid to Families with Dependent Children (AFDC) programs be "deferred for further negotiations."

In the federalism initiative he offered last month, Reagan asked the states to take over those two programs in return for the federalization of all Medicaid costs. Because most governors want to see the federal government finance all income maintenance programs, the association asked to defer the decision on food stamps and AFDC, offering instead to take over a variety of less controversial domestic programs whose costs would equal or exceed the Medicaid burden going to Washington.

According to Snelling and others, Reagan also made no objection to their suggestion that federal income tax revenues be used to support the swapped programs for a transition period and perhaps beyond, nor to the idea that the transition funds be distributed to equalize resources of rich and poor states--on which he has previously demurred.

But Reagan made it clear that he still believes welfare is best handled by the states. According to participants, when Kentucky Gov. John Y. Brown (D) suggested that a state takeover of AFDC would lead to a patchwork system, Reagan responded that the present system has "50 different levels of benefits."

But Reagan clearly was eager to enlist state support for his initiative. According to Williamson and others, he said the governors' proposal "opened the door" to useful negotiations. He held out the possibility that if they can agree "on a small swap" now, larger changes could come in future years.

The federalism initiative was also endorsed in principle yesterday by the National Association of Counties, but, like the governors, they urged that all income maintenance programs be federalized.

Snelling told Reagan the governors were going to be fighting his fiscal 1983 budget cuts on Capitol Hill, a statement Reagan received without comment. Tennessee Gov. Lamar Alexander (R), one of the main supporters of the federalism initiative, said the reason there was "not much budget talk" was that "none of us expects the president's budget to pass." The governors began the negotiation process Sunday. Caucuses that continued late into Sunday night produced a bargaining-position paper drawing heavily on ideas of Georgia Gov. George Busbee (D), Utah Gov. Scott M. Matheson (D) and Sen. David Durenberger (R-Minn.).

It was approved at a closed session of governors yesterday morning by a 36-to-5 vote. The five dissenters, all Republicans, argued that it should have included more elements of the original Reagan proposal.

The governors said they wanted to keep highway programs out of the swap, because they are financed from their own trust fund.

Before the White House meeting, several governors said privately they expected Reagan would reject the swap and urge them to come further toward his original proposal as part of the bargaining process.

But Williamson, signaling the conciliatory mood Reagan would later display, said that overall, it represented "a positive move" toward agreement with the administration view.