After letting his party's presidential front-runner twist in the wind for nine days, Rep. Harold Washington, the Chicago Democratic mayoral nominee, finally returned Walter F. Mondale's repeated telephone calls yesterday, easing tensions between Mondale and many black leaders, but not necessarily healing all wounds.

"We were very encouraged by the call," said Mondale's chief adviser, James Johnson, clearly relieved by this first signal that Washington, who is black, was willing to forgive--if not forget--the fact that Mondale, who gets considerable support from blacks, had campaigned against him.

In yesterday morning's eight-minute conversation Mondale offered his congratulations, Johnson said, and Washington asked Mondale to go to Chicago to help him campaign against his Republican opponent, Bernard E. Epton, in the April 12 general election.

Mondale, who had been angling for days for just such an invitation, happily agreed. No date has been set, Johnson said, adding, "The tone of the conversation was excellent."

Mondale endorsed Cook County State's Attorney Richard M. Daley, son of the late mayor Richard J. Daley, in the Feb. 22 primary, and campaigned for him despite requests from numerous black Democrats that he not actively oppose what they considered the best chance ever for a black to become mayor of the nation's second-largest city.

Since Washington's surprise victory over Daley and Mayor Jane M. Byrne, who was endorsed by Sen. Edward M. Kennedy (D-Mass.), some black political leaders are citing the Chicago primary as a prime example of how blacks are taken for granted in the party they have supported for so long.

"The fact is that it Washington's campaign was a joke around the DNC Democratic National Committee when we were meeting with Mondale and Kennedy about their going to Chicago to campaign," said Rep. Mickey Leland (D-Tex.), chairman of the DNC's 52-member Black Caucus, which asked Mondale not to campaign for Daley. "People were taking him for granted because he was black. They can't take candidacies by black people lightly any more."

Mondale maintains that he had pledged his active support to Daley before Washington entered the race and would have appeared weak and vacillating if he had broken his word.

Mondale, Jimmy Carter's vice president, also wanted very much to defeat Byrne, who had endorsed the Carter-Mondale ticket early in the 1980 nomination fight and then switched her support to Kennedy.

"Keeping his word was important, not in terms of trying to react to polls suggesting that Mondale is not seen as a strong person . But it's the kind of thing that someone who's running for president has to do," said George A. Dalley, Mondale's deputy campaign manager.

"There was a specially heightened feeling that developed from the Jane Byrne double cross and a long relationship between the Daley family and Mr. Mondale," Dalley said. "It is a special case. Our disposition in this campaign would be to stay out of primary campaigns in the future."

On Monday, DNC Chairman Charles T. Manatt is to meet with Washington in Chicago in a show of party solidarity following the bitter primary, which had racial overtones so strong that some question the Democrats' ability to unite in the general election campaign.

Johnson, Mondale's chief adviser, has conferred with Manatt about the trip, and said he is hopeful that Manatt's visit may help smooth things over between Mondale and Washington, even though the trip was not designed to do so.

"Manatt will emphasize the importance that the national party places on this election," Johnson said. "Manatt will say that he is speaking for us as well as for everyone else."

Washington already had accepted congratulations from the other major presidential contenders who called, including Kennedy, who has pulled out of the 1984 race and who did not campaign for Byrne, and Sen. Alan Cranston (D-Calif.), who endorsed Washington.