President Carter has intensified pressure on major corporations to comply with his voluntary anti-inflation program, asking the heads of big companies for explicit assurances that they will observe his price guidelines.

At the same time, at a breakfast meeting with reporters, Carter said the chances of a recession or depression next year are slim, provided there is at least moderate compliance with his wage and price guidelines.

Only if there is a "complete and abject failure in our anti-inflation program" is recession or depression "a possibilty. I won't say likelihood." He went to say that he thinks the anti-inflation program will be a sucess.

Carter's comments came a day after an inflation chief, Alfred Kahn, had warned of a "deep, deep depression" if the anti-inflation program failed.

In a related development, Federal Reserve Board Chairman G William Miller told a Senate committee that the chances of a recession next year have been reduced by moves to protect the dollar and boost interest rates, a statement disputed by many economists.

But Miller's predictions on inflation and economic growth for next year were somewhat more pessimistic than the administration's.

The president's unusual letter to major corporation heads said that general statements of support from business leaders are not enough.

"I am asking your company for an explicit statement of your commitment to comply with the price standard." Carter said in a letter sent Wednesday. He asked the corporate leaders to "send me your personal response . . . as soon as possible."

The Council on Wage and Price Stability will monitor all companies with annual sales of more than $500 million to insure that they are complying with the program.

Carter generally wants companies to hold their price increases over the next 12 months to half a percentage point below their average price increases in 1976 and 1977, with some exemptions.

In his breakfast session with reporters, Carter played down talk of recession. "I just don't think we are going to have a substantial economic set-back next year," he said. "I anticipate success with the anti-inflation program. "He held to the administration's prediction that the economy would grow about 3 percent next year, fast enough to keep the unemployment rate from rising above 6 percent where it has hovered much of this year.

A growing number of economists, including some in the administration, think that the recent sharp increases in interest rate triggered by the Federal Reserve Board-as part of a coordinated effort to fight inflation and prop up the dollar-will choke off the expansion and throw the economy into a mild recession.

At the breakfast meeting. Carter said. "If there is one group that has an extreme diversity in analysis, it is economists."

Federal Reserve Chairman Miller, testifying before the Senate Banking Committee, said that the Fed's recent interest-rate raising moves have lessened the chances that the economy will go into a tailspin.

Miller said that international money markets were unstable and that the instablility was spreading into domestic financial markets. That instability would have caused businesses to postpone or cancel expansion plans, which in turn would have increased the likehood of a recession.

But his projection of economic growth and inflation next year are a little more pessimistic than the administration's.

Miller predicted that the economy would grow between 2 1/2 percent and 3 percent in 1979. The Carter administration projects 3 percent or more.

Miller also predicted that inflation would run between 6 3/4 percent and 7 1/2 percent next year. Carter projects inflation between 6 and 6 1/2 percent.

Asked about the discrepancy by Banking Committee Chairman Sen William Proxmire (D-Wis), Miller said. "I can't say. We've done our own independent estimates . . . We just came to a different conclusion."

Miller also said he hoped the administration and Congress could reduce the federal budget deficit to $20 billion or less in 1980. Carter has pledged to hold the deficit below $30 billion.

Carter told reporters yesterday that he would prefer lower interest rates but that before interest rates can be lowered inflation must be reduced.

And he pledged to hold his course in his fight against inflation by cutting spending and urging complaince with his voluntary program-regardless of "temporary aberrations or pressures from interest groups."

In another development, White House spokeman Jody Powell said that Carter had hold him he is not aware of any proposals to alter the 7 percent wage standard in his anti-inflation program.

The Washington Post reported yesterday that the administration is considering changing the treatment of the cost of maintaining existing fringe benefits so that the 7 percent standard would not bite quite so hard.

Unions have complained that government ordered increases in pension cost to employers and rising health insurance premiums will eat up large chunks of the 7 percent standard, leaving little room for wage increases. The 7 percent standard applies to wages and fringe benefits.

Powell said there are likely to be similar reports in the weeks ahead as the administration attempts to apply the standards to particular cases. "We will be considering in the broadest sense, a lot of things, but to imply we are going to accept [them] is wrong," Powell said.