President Carter, who said on Thursday that America is "turning the tide" in the fight against inflation, conceded yesterday that the cost will be a recession sharper and more severe than he had expected.

For months, the president had predicted the decline in the economy would be short and mild, but yesterday he agreed that it "is going to be a serious problem."

"We've got serious recession prospects, steeper than we expected. But we're doing everything to alleviate the problem with individual Americans and also to shorten it," Carter said.

The president spoke to reportears outside CBS News here after taping the "Face the Nation" program that is to be aired on WDVM-TV-9 today. Carter and his wife, Rosalynn, flew to the Camp David presidential retreat for the weekend.

His remarks came a day after the Commerce Department reported that leading economic indicators had plunged 4.8 percent in April -- the largest decline in the 32-year-old index. The report set off new fears of a deepening recession.

As he campaigned in Columbus, Ohio, Thursday, Carter was more upbeat about administration econonic policies, telling cheering crowds:

"We're turning the tide on the economy from a nation of worldwide inflation and from escalating interest rates to a nation determined to bring inflation under control."

Mortgage interest rates and the prime lending rate that banks give their best customers have fallen several percentage points since March 11, when Carter announced his latest effort to stem inflation.

Carter said he expected these trends would help revive the depressed automobile and home construction industries.

But what the president seemed to suggest yesterday was that the price of these inflation-fighting efforts would be rising unemployment in the short term.

"Of course, we've got the carefully defined government programs already on the books," he said. "It will help to minimize the damage to a family that is afflicted with unemployment. And we'll try to preserve those programs and strengthen some of them, particularly youth employment, home construction, that sort of thing."

Meanwhile, yesterday, Carter was sharply criticized by Senate Majority Leader Robert C. Byrd (D-W. Va.) for attempting to have some appropriations shifted from defense to social programs in the federal budget now taking shape on Capitol Hill.

Byrd indicated he felt the president's intervention threatened to send Congress on another "spending spree," ending any hope of balancing next year's budget.

Carter urged members of Congress Tuesday to defeat their Budget committees' compromise spending plan, saying it included too much money for the military and not enough for programs designed to help "deteriorating cities" and provide jobs.

A perturbed Byrd yesterday said, "I'm just concerned about the exaggerated emphasis and attack on the budget process. To quibble over tweedledum and tweedledee is destructive of this process.

"If the budget process goes down there will be no discipline, no amends for those who are afraid we will spend a penny or two more on defense (or those who fear) we will go hog wild on spending for domestic programs."

Byrd recalled that Carter had set a balanced budget as his goal. And he noted that the budget proposals are tentative and can be adjusted by Hill committees which "can make amends for the economic situation as we find it."

Byrd said Carter's actions on Tuesday had created such ill-will in the Senate that it no longer seemed likely he would get approval of this proposal for an oil import fee to raise gasoline 10 cents a gallon.

The fee is urgently needed as a "modest" measure to spur energy conservation, Byrd said. He said he would support it but feared it would fail now because of some senators' anger with Carter and because the administration had failed to explain its merits properly.