The number of Americans a month or more late in making mortgage payments rose to a record high during the first three months of 1983, indicating that the recession continued to hurt hundreds of thousands of homeowners. The delinquency rate of 5.84 percent represents 1.3 million loans, a figure that both surprised and disappointed the nation's lenders.

The number of foreclosures in progress during the first quarter also was up slightly, to a record 0.71 percent--or 143,000--of the more than 8 million home loans surveyed for the report, issued by the Mortgage Bankers Association.

On the bright side, the number of foreclosures initiated during the quarter dropped for the first time in a year and a half, and long-term delinquencies--by homeowners more than three months late with payments--remained unchanged at 0.84 percent.

The drop in first-time foreclosures and lack of change in long-term delinquencies may indicate that the worst is over, according to the bankers association. But its executive vice president, Mark J. Riedy, said that the survey results are "a mixed bag."

"The numbers aren't as good as I hoped they would be," Riedy said. "I just didn't think the one- and two-month delinquencies would go up."

Congressmen who back mortgage relief legislation being considered in both the Senate and the House said quick financial aid for homeowners is needed as much as ever.

"The level of foreclosures is still too high, and with little change in the level of unemployment, it's clear that the number of foreclosures will increase," said Sen. Donald W. Riegle Jr. (D-Mich.).

Rep. Henry B. Gonzalez (D-Tex.) charged that housing and unemployment figures nationally are misleading because of Reagan administration "statistical juggling" and said "there's no question that a continuing emergency situation exists throughout the country."

Legislation sponsored by Gonzalez would provide $760 million in loans to help about 100,000 homeowners facing foreclosure, he said. A similar measure is part of the Senate housing bill now being considered.