The annual convention of Operation PUSH tonight turned into a pep rally for a black presidential candidacy starring the Rev. Jesse Jackson.

As a crowd of more than 2,000 loyalists chanted, "Run, Jesse, run!" Jackson, the founder of PUSH, laid out a rationale for such a candidacy, but said afterward he is weeks away from a final decision.

"A black presidential candidacy is a test of the moral character of the nation," Jackson thundered to his followers, who punctuated his speech with amens and shouts of "Go, Rev."

Outside the ballroom, supporters snapped up buttons, with Jackson's face and the "I Am Somebody" slogan he espouses, while inside they anted up cash, some as much as $100, to finance his deliberations.

Jackson heard himself introduced as "a God-man" and a "prophet of God." And California Assemblywoman Maxine Waters reflected the spirit of the evening when she said, "I came here to say to the Rev. Jackson, whatever he decides, . . . many of us will stay with him . . . . I'm here to say, Rev, let's go get it."

Jackson did nothing to dampen the enthusiasm with his speech. Sounding much like a man preparing to run for president, he said a black candidate would put both the Democratic Party and the nation "on trial."

"The real question is whether white America can put character over color and reason over race and judge a black candidate by the same standards that it judges all other candidates," he said.

He dismissed as "diversionary" arguments that a black candidacy would divide the Democratic Party, then said that a black "should run a serious primary campaign and seek the Democratic nomination."

The civil rights leader said a black candidacy "would dramatically increase" black registration and turnout, and that this could be the key not only to Democratic hopes of carrying the White House but also of recapturing the Senate.

"Running must become a strategy," Jackson said, and the crowd soon responded with "Run, Jesse, run!"

"If this audience is a barometer of blacks across America, the announced Dermocratic candidates are in serious trouble with black voters," said Atlanta City Councilman John Lewis, a veteran of the civil rights movement.

As he left the podium, Jackson said he was gratified by the response but called the support of the people just "one dimension" of mounting a campaign. He said a decision was "premature."

Jackson had harsh words for President Reagan's policies, especially on Central America. He said that Reagan's recent actions in that area are "nothing but preparation to send the black, the brown and the white poor to fight and die to protect rich interests."

He added that neither the Soviets nor the Cubans are to blame. He also said unrest in the region is the "result of centuries of exploitation" and "a sad record" of U.S. intervention to protect "big business and corrupt dictators."

Tonight's political revival culminated several days of growing enthusiasm for Jackson's possible candidacy.

There were whoops of delight from convention delegates when Mayor Richard Hatcher of Gary, Ind., asked in his luncheon speech, "If not now, when? If not Jesse, who?"

"We need a prophet," the Rev. Cameron Alexander of Atlanta said at a prayer breakfast, pointing at Jackson. "How long do we have to wait? Is it really a White House, or is it our house? Open up the door or we gonna kick it down!"

Many blacks here scoff at the idea that a Jackson candidacy would hurt the most liberal Democratic candidate and that blacks would lose as a result.

"Nothing you could do could hurt black people more than we are hurt now," said Mayor Earl Lucas of Mound Bayou, Miss.

Even Atlanta Mayor Andrew Young, a long-time opponent of a black candidacy on the grounds that it would make blacks outsiders in the Democratic nominee's campaign, is encouraging Jackson to consider running. "The question is what can be done to assure a Democratic president right now," Young said. "To elect any Democrat president, you need 60 to 70 percent turnout among black voters. And one thing that's helping us register black voters is all the hoopla around Jesse running."