Alan Greenspan, an influential economist who often advises the Reagan administration, said here today that the nation's economic recovery will slow dramatically in the next six months because of continuing federal budget deficits.

The economist told the National Governors' Association that presidential politics will prevent agreement on the painful steps needed to reduce a series of expected $200 billion deficits, and he called for a "domestic economic summit" between congressional leaders and whoever wins the White House next year.

Greenspan, who chaired President Reagan's Commission on Social Security and was President Ford's top economic adviser, said the persistent deficits cannot be cut without significantly reducing entitlement programs such as Medicare. The federal health-care program for the elderly cannot survive unless some patients with high incomes are excluded, he said. The proposal is certain to arouse fierce opposition.

Meanwhile, an open letter circulating here among Democratic governors blamed the "failure" of administration economic policy for the high deficits, and criticized Vice President Bush for "misleading" people in his Sunday speech to the conference. Bush contended that the robust recovery will continue.

Greenspan, delivering a much bleaker forecast than did Bush, said the economy is growing rapidly now because business inventories were depleted last winter, and because of a boom in short-term consumer purchases that do not rely on bank financing. But he said the recovery "will begin to slow down at a fairly dramatic rate as we get into 1984. The reason . . . is that interest rates are too high" and will prevent the kind of long-term investments that would fuel continued economic growth.

"I wish I could say I could see some resolution of this problem through November, 1984, but as the political season gets closer," a possible solution "falls further into the past," Greenspan said. "There is something terribly corrosive about this budget deficit . . . . There is no way to resolve this issue without political pain."

Greenspan, who designed the package of tax increases and benefit cuts that rescued the ailing Social Security System, said federal officials must agree on some combination of higher taxes, reduced defense spending and curtailments in entitlement programs. He singled out Medicare, which is financed largely by the Social Security tax and provides benefits for 29 million elderly or disabled recipients.

Medicare benefits "ultimately will have to be means-tested," said Greenspan, who is president of Townsend-Greenspan & Co. "I do not see how we can finance the existing law . . . . We are committed to provide resources which I suspect are not there."

Sources said Greenspan has discussed the Medicare problem with the administration, which recently was told by an advisory panel that the Medicare Trust Fund faces bankruptcy by 1990 and an eventual deficit of $200 billion to $400 billion.

Reaction to Greenspan's comments split along partisan lines.

"Can we continue to cut domestic spending, raise defense spending and finance tax cuts by borrowing, and hope to ever bring down that deficit?" asked Wisconsin Gov. Anthony S. Earl (D). "Defense spending is not held to nearly the same scrutiny as domestic programs. Indeed, it seems to be exempt from any scrutiny at all."

But Washington Gov. John Spellman (R), citing rising housing starts and lower inflation, said, "I'm more optimistic now than I've been in 2 1/2 years. All the indicators are positive." He called the deficit "a largely psychological problem."

Nebraska Gov. Bob Kerrey (D) took a much tougher tone toward the administration in a letter he began circulating for signature among his Democratic colleagues. Addressed to Bush, who told the governors Sunday that Reagan's policies had produced a surging economic recovery, the letter said, "Your program of tax reductions and increased defense funds failed to produce anything other than a $200 billion deficit . . . . "

The Kerrey letter also took issue with Bush's defense of administration policy in Central America. Kerrey said Bush's claim that the president's emphasis has been on economic and humanitarian aid, not military training, was false. "You intentionally misled us with your statement," Kerrey said.

Late today, Environmental Protection Agency Administrator William D. Ruckelshaus was welcomed warmly by governors of both parties who had clashed frequently with his predecessor, Anne M. Burford. Ruckelshaus promised to move swiftly on the problem of acid rain, saying he hoped to have recommendations from an EPA task force by Labor Day and to hammer out a policy with the White House by mid-September. He assured the governors that he would consult first with an acid-rain task force that they appointed today.

Ruckelshaus agreed with the governors that more money must be found for the EPA's Superfund to clean up toxic waste sites. "We have asked for an extra $100 million for next year," he said, "and we may need more than that to stay on schedule."