Frank Mankiewicz, who guided National Public Radio (NPR) to national prestige and popularity in the past five years but spent the past few weeks battling criticism of his financial management, announced yesterday he is stepping down from the top post at the network.

The announcement, made at the 12th annual Public Radio Conference in Minneapolis, came after weeks of debate about Mankiewicz's responsibility for the unexpected $5.8 million deficit facing the country's only national public radio network.

After reading a statement that praised the NPR board for bringing in a transitional chief operating officer, Mankiewicz, 58, said, "I will not be at National Public Radio for long. I have been there 5 1/2 years and I have been talking some time about not staying forever."

The temporary successor to Mankiewicz, who will retain Mankiewicz's title of president, was said by some sources to be Ronald C. Bornstein, a University of Wisconsin administrator who has been active in public broadcasting since 1956. Bornstein is acting chancellor of the University of Wisconsin-Extension and director of the university's division of telecommunications. He was a vice president of the Corporation for Public Broadcasting from June 1980 to May 1981.

Bornstein confirmed he had talked with Myron Jones, NPR board chairman, in Minneapolis Monday. "But I have not been formally approached, nor have I decided what to do if I was formally approached," he said. "I wouldn't characterize the conversation with him as an offer."

National Public Radio provides programming to 279 noncommercial member stations with an estimated audience of 7.7 million. Mankiewicz was the campaign manager for George McGovern in the 1972 presidential race, and was press secretary to Robert Kennedy in the 1968 presidential campaign.

Since Mankiewicz became NPR president in August 1977, the annual budget has tripled. In recent weeks, it was reported that NPR had $5.8 million less in funding than this year's $26.3 million budget called for. Last month, in the first attempt to balance the 1983 budget, the network fired nearly 10 percent of its 400 Washington employes and announced the cancellation of two programs, "The Sunday Show" and "Jazz Alive."

The flagship programs of the 13-year-old nonprofit membership organization are the daily "All Things Considered" and "Morning Edition." Both originate in Washington and are considered sacred and probably will not be affected by the cuts. "If they are cut, NPR turns into a parking lot--that's 80 percent of what we do here," said one employe.

Commenting on the financial upheaval, Bornstein said, "For the staff and system it is a regrettable incident and the important thing is that the system, the management and the board work together cooperatively. NPR is a vital part of American communications."

In the past week Mankiewicz survived two no-confidence votes taken by the NPR board. The board, which is meeting in Minneapolis through today, represents the member stations. The members, who were told at the Minneapolis meeting that the deficit had grown from original projections of $2.8 million to $5.8 million, were scheduled to vote today on the board's recommendations to cut $1.5 million from the NPR programming budget and to assess member stations programming fees totaling another $1.5 million. Each station, the board recommended, could be charged $5,500 to $8,400, depending on size.

Other recommendations called for eliminating the weekend version of "All Things Considered" as well as NPR Plus, which includes a daily package of news briefs, cultural affairs programming and "Dateline," a half-hour news show that has picked up 60 stations since it debuted Jan. 3. The board also is considering an on-the-air national fund-raiser.

Many of Mankiewicz's critics blamed the financial crunch on his development of new programs without funds to pay for them. "It looked like a wonderful new horizon . . . It seemed only natural that business and financial sources would look at it and say, 'It's wonderful,' " one veteran producer said yesterday.

Mankiewicz pinpointed problem areas as cutbacks in federal funding, the recession and a slow return on profit-making ventures.

"I wish the recession had been over a year earlier," he said. "When you have to make budget adjustments, then you can't quarrel with the fact that something was wrong. It happened on my watch. We took a gamble and it didn't work."

Exactly when Mankiewicz will leave is uncertain. "When we are through this difficult time and the mechanisms you approved have been put in place, it will then be time for me to withdraw from any active managerial responsibilities . . ." he told the conference.

Mankiewicz said that during the transition period he will be the system's chief fund-raiser and liaison with Congress and federal agencies.

Jones, the board chairman, yesterday said the transitional chief of the network will serve for six months and "will have full responsibility for the day-to-day operational and managerial decisions and will report directly to the board."

It was not clear how Mankiewicz's announcement would affect two executives he hired: Barbara Cohen, vice president and managing editor of news and information, and Tom Warnock, executive vice president.