The Carter administration yesterday raised the maximum allowable interest rate for mortgages financed by the Federal Housing Administration and the Veterans' Administration to 10 percent, the highest in the 45-year history of the two programs.

The increase, from the 9.8 percent level that had prevailed since last June, was designed to prevent a dryup of federally backed mortgage loans in the face of sharply higher conventional mortgage rates. The change becomes effective on Monday.

The move came as, separately, the Federal Reserve System's policy-setting Open Market Committee disclosed it voted against any further tightening of monetary policy at a meeting on March 20, despite a push for firming by four of its 10 current members.

The minutes of the March 20 meeting, made public yesterday after the required month of secrecy, showed the majority voted to continue previous policy without change because it feared the economy was heading toward a recession. Nevertheless, the split was the largest in 1 1/2 years.

The committee's action was revealing in light of the Carter daministration's abortive attempt last week to prod the Fed into raising interest rates still further. The panel met again this past Tuesday, but apparently decided once more against further tightening.

Meanwhile, Fed Chairman G. William Miller softened a statement has made on Thursday that the Fed would have to consider tightening monetary policy again if the economy grew at more than 2.5 percent annual rate in the second quarter of this year.

Miller said yesterday he personally would consider the economy "on track" if the overall growth rate averaged 2.5 to 3 percent for the first half of this year. Since the first quarter's growth rate was recorded at an 0.7 percent pace, that would allow substantially more room.

Miller's statement on Thursday had appeared to conflict with predictions by a Commerce Department economist that the economy was likely to bounce back in the current quarter and possibly reach a growth rate of 3 percent or more. Fed sources said Miller did not intend to be so precise.

The March 20 decision by the Open Market Committee ordered Fed money managers to hold the key federal funds rate within a range of 9.75 percent to 10.5 percent-a slightly wider band than the group had set previously, broadened to account for heightened uncertainties.

The document reported that many members of the committee thought the Fed's staff had been "overly optimistic" in projecting moderate growth through the second half of 1979 and "believed that the chances of a recession beginning before the end of the year or early 1980 were faily high."

The panel also concluded that the then-new acceleration in inventory building-which has been of concern to Carter administration policymakers-"represented prudent business behavior" in view of expected strikes and other factors "and no a major shift away" from businessmen's earlier caution.

The committee appeared to be split three ways at its March 20 meeting, with a portion of the panel favoring holding monetary policy steady, some urging a more restrictive stance and others seeking an easing of policy to help ward off a recession.

The four members who dissented favor of a more restrictive policy included board members Henry Wallich and Philip E. Coldwell; Monroe Kimbrel, president of the Federal Reserve Bank of Atlanta; and Paul A. Voilcker, presiden of the New York Federal Reserve Bank.

Some observers speculated it was this obvious dissension within the committee that encouraged top Carter administration policymakers to launch their campaign for a tightening of interest rates at last Tuesday's session-a move the panel apprently rejected.

The increase in maximum lending rates for FHA and VA mortgages will apply only to loans for purchases of single-family homes. The rates for multi-family units will continue to be 9.5 percent, according to the Department of Housing and Urban Development.