Democratic mayoral nominee Harold Washington said today that former vice president Walter F. Mondale "has some serious explaining to do" for backing Cook County prosecutor Richard M. Daley in last Tuesday's bitter mayoral primary.

Rep. Washington (D-Ill.) told a jammed news conference in his cramped downtown headquarters that "Mondale has debts to pay, and one of the things that disturbs me greatly about so many leaders in this country . . . is they take, but they don't give. Well, if you take from my people, you've got to pay."

Washington's blunt comments made clear that, as far as he is concerned, Mondale, the front-runner for the 1984 Democratic presidential nomination, blundered when he endorsed Daley and campaigned for him in the closing weeks of the Chicago campaign. The son of the late, longtime mayor came in third in the primary, behind Mayor Jane M. Byrne, who had been endorsed by Sen. Edward M. Kennedy (D-Mass.).

Washington, who won on the strength of a large black voter turnout and a split among white voters, also asked that the racial question be avoided by the media in his coming campaign against Republican Bernard E. Epton. "I urge you to leave this thing alone," he said. "It is not an issue to play up. It is a very, very volatile situation."

If Washington wins the general election on April 12 he will become the first black mayor in the 150-year history of Chicago, which has a 41 percent black population.

Washington said he had received a congratulatory call from Sen. Alan Cranston (D-Calif.), who backed him in the race. However, he said that Cranston did not ask him for support in his presidential campaign.

Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) said at a luncheon in Washington today with editors of The Washington Post that "Cranston locked on to a big and important win in Chicago, and that's going to improve his chances."

Washington's bitterness toward Mondale held center stage at his news conference here.

"Mr. Carter and Mr. Mondale elicited my support in the 1st and 2nd Congressional Districts in 1980 . . . . I spent time and money and we brought in a 93 percent vote.

"Then I find Mr. Mondale wants to endorse someone else" in the Chicago race. "There's a certain thing called gratitude in this business. I've said before that politics ain't beanbags, and if they think it is, don't play with me."

In an interview with The Post last week, Washington said that Mondale's endorsement of Daley was "a typical attitude of a lot of white politicians who simply don't assume they have a debt to blacks when they get black votes."