Former representative Donald Fraser, a Minnesota Democrat who lost a bitterly contested Senate primary race last fall and then was turned down for a job with the State Department, has returned home to seek election as mayor of Minneapolis.

Fraser, 55, an eight-term liberal congressman generally regarded as an authority on international relations and human rights issues, has been working part time since January as a counsel to a congressional study group, Members of Congress for Peace Through Law.

He raced back to Minneapolis last Saturday to win a second ballot endorsement for mayor at a Democrat-Farmer-Labor (DFL) Party city convention one day after incumbent DFL Mayor Albert Hofstede announced he would seek reelection.

Fraser's chief competitor for the endorsement was veteran state Rep. James Rice, who is expected to challenge Fraser in the DFL primary election in September. Rice is closely allied to millionaire businessman Robert Short, one-time owner of the old Washington Senators' baseball franchise who ran unendorsed to defeat Fraser in the DFL primary election for the Senate last September.

Short narrowly won that race by viciously attacking Fraser's liberal views on abortion and public spending and his environmentalist stand on preserving a large wilderness area in northern Minnesota.

But the DLF Party was hopelessly divided after the primary, and Short subsequently lost in the general election to Republican David Durenberger.

A matchup between Fraser and Rice undoubtedly would rekindle intraparty rancor. During Rice's address to the DFL convention last weekend, for example, some delegates held up signs that read "Stop Short."

Fraser's hopes of landing a diplomatic post with the Carter administration after his loss to Short were doomed by political animosities that not even Vice-President Mondale, his longtime friend, could dispel.

Mondale and his top aides encountered stiff opposition to hiring Fraser from the White House and the State Department, where Fraser were considered to be something of a trouble-maker.

The administration recently offered to appoint Fraser as a member of the U.S. delegation to the U.N. General Assembly, but Fraser declined, according to a Mondale aide. Fraser would have been one of three delegates from the private sector, according to the State Department. CAPTION: Picture 1, DONALD FRASER; Picture 2, REP. JAMES RICE