Fresh from his triumph Tuesday over two white candidates for Chicago's Democratic mayoral nomination, Rep. Harold Washington says "I definitely favor" a black candidate's entry into next year's presidential primaries with the aim of expanding black influence at the Democratic National Convention.

Washington made clear that his dissatisfaction with his party is deep, saying at one point during an interview that "I can advocate leaving the Democratic Party . . . . "

But he asserted that he prefers to work inside the system and said the emergence of a black-candidate movement "could keep them nervous." He said he is backing no particular person, but said exploratory talks among black leaders are "very serious."

Black legislators, mayors, congressmen and other Democratic leaders have been meeting with increasing frequency in various cities in recent months to consider a black-candidate movement. Washington's upset victory over Mayor Jane M. Byrne and political heir Richard M. Daley has infused these talks with a new sense of excitement, interviews with several black leaders around the country today made clear.

The two-term congressman's victory was built on a massive registration drive that added perhaps 200,000 black voters to the city's rolls. The success of that effort was one part of his winning formula that has attracted attention from black politicians elsewhere.

Black leaders said the strategy sessions are beginning to focus on whether there should be separate "favorite son" black candidates in various states or whether a national candidate can be found who is acceptable to the moderate and more activist members of the general leadership coalition.

Carl Holman of the National Urban Coalition said that in years past officeholders generally did not take the lead in such talks. But this time, said one person involved in the current discussions, "The politicians are expressing interest in having a politician do it if there is a national candidate."

Washington refused to discuss who he thought should take the lead role if the movement idea jells.

But the Rev. Jesse Jackson, who has been predicting that a black will run for president in 1984, said he favored a single, nationwide candidate rather than a movement headed by several favorite-son candidates. The candidate, Jackson said, "must have the ability to galvanize the black masses and the ability to interpret the national black agenda."

The last major black candidate to campaign across the country seeking the Democratic presidential nomination was then-Rep. Shirley Chisholm (N.Y.). She lost the nomination to Sen. George McGovern (S.D.) in the first round of balloting at Miami Beach in 1972.

Reagan administration cutbacks in social programs, compounded by recession-shrunk local budgets, have fueled black impatience with the national Democratic leadership, interviews showed.

Among the most outspoken on this score are black leaders of northern cities like Chicago, where industrial jobs have declined and unemployment among black breadwinners can exceed 30 percent.

Washington, who faces Republican Bernard E. Epton in the April 12 general election in a city where no Republican has occupied City Hall in 50 years, can already taste the problems facing Chicago.

"There is a $100 million shortfall coming up in the city, plus another $100 million from the school board. That seems to be a standing figure from the school board. You can't squeeze any more from corporate business; you can't get into regressive areas like sales and utilities taxes. In the short range, we're going to have to beg. That's it!

"Where do we cut? . . . health . . . sanitation . . . fire . . . police . . . . It's going to be a draconian situation."

So why should a 60-year-old, chain-smoking congressman want to leave the ironclad safety of the 1st Congressional District, the nation's oldest and largest northern black congressional district, to become mayor of a Windy City so buffeted by economic storms?

"The need and the desire. I was not ambivalent. The only question was--could I win? Once I was convinced I could win, there was no hesitation at all. Period. It was that simple.

"What's public service all about? If I could turn this city around in four years--wow! Who wouldn't want to do that?"

While his shoestring campaign ran on the contributions of thousands in a "people's movement," the man at the center is a hard-edged politician, seasoned by 20 years of Chicago-style office-holding, first in the Illinois legislature as a handpicked member of the Daley machine, then as an anti-machine insurgent in the 1st district. Caution is the byword of the machine and caution remains a dominant trait in Washington, as he made clear when recounting what preceded his entry into the mayoral race.

Beginning in mid-1981, private polls told him that blacks in South Side and western wards, fed up with white rule at City Hall, would vote for any qualified black candidate. "They didn't even ask who it might be. It was clear what was going on. It was anti-Reagan and anti-Byrne."

Then came the autumn voter registration effort. "The drive was in full swing at the registering outposts . . . . For the first time, we outregistered whites, 2 to 1. Approximately 150,000 blacks were registered, and it was clear--it was there."

Next was the Nov. 2, 1982, gubernatorial election, with GOP Gov. James Thompson running against Adlai Stevenson III, stolid heir to his father's legacy as a witty, liberal governor. "Thompson thought he'd get 30 to 35 percent of the black vote--he got 7 percent. Seventy-two percent of blacks voted and 93 percent of that vote went for Stevenson," Washington said.

Careful analysis of past elections indicated that if Washington ran against two whites he could turn out enough black votes to win.

Washington said, "I tried to get Rep. Dan Rostenkowski D-Ill. to run by appealing to his Polish pride. But he didn't bite the bullet."

Instead, Richard M. Daley, Cook County prosecutor, entered the race against Byrne in hopes of recapturing City Hall, where his father, Richard J., had ruled for 21 years. Washington had his third candidate.

Washington sees no contradiction now in running as a unity candidate in what some might term a triumph of race politics. He makes the point that so long as blacks were shut out of power the city was racially divided.

"There is no contradiction," he said. "You have to win . . . within the bounds of decency . . . It had nothing to do with color. It was just a question of winning.

"On the other hand, we made it very clear, it is a people's campaign. We want everybody in it."