Angry about the selection of the Illinois state comptroller as vice chairman of the Democratic Party over the nominee of the party's black caucus, 300 black leaders have agreed to establish a process for selecting a single black nominee for local, state and congressional races.

"We have structured a process for ensuring that . . . we are getting genuine representation of black interests through those active in the parties as black people and not as just another black face," said Del. Walter E. Fauntroy (D-D.C.), president of the National Black Leadership Roundtable, which met here over the weekend.

"The process will go into effect in a race where there is more than one black candidate for office and there is a question of one of them receiving aid from outside the black community for the purpose of limiting black leverage," Fauntroy said.

After determining which candidate to support, the national black leaders would lend their support to that single candidate, get black fraternal and labor organizations to work for the candidate and try to raise funds for that candidate.

Some voiced concern about the procedure.

"Are they saying 300 people are going to decide for all black America who will run for office?" asked Roland W. Burris, the Illinois comptroller who defeated Gary, Ind., Mayor Richard G. Hatcher to become vice chairman of the Democratic National Committee. "That doesn't make sense."

"I see this kind of criteria further dividing the black nation along the lines of the Burris victory over Hatcher," said one observer who attended the political meeting at the Roundtable convention.

"How can you decide who is the best person to represent the interests of black America?" he asked. "It creates a situation where only a certain kind of black can run for office and I'm not sure that's a good situation."

Although the move was sparked by Burris' defeat of Hatcher, black Democrats acknowledge that their plan would not have kept Burris from winning the vice chairmanship. Inside the DNC whites can outvote blacks, and a black candidate who has white support can defeat a black candidate who has total black support.

Among the black leaders attending the weekend convention were Coretta Scott King; the Rev. Jesse L. Jackson; Fauntroy; Hatcher; Robert Farrell of the National Black Caucus of Local Elected Officials; Rep. Charles B. Rangel (D-N.Y.); Rep. William H. Gray III (D-Pa.); Robert L. White, of the National Alliance of Postal and Federal Employes; Dorothy I. Height, president of the National Council of Negro Women; District Mayor Marion Barry; M. Carl Holman, president of the National Urban Coalition; Clarence Mitchell III, president of the National Black Caucus of State Legislators; and C. Delores Tucker, chairman of the DNC's black caucus.

Meanwhile, Burris, met yesterday with party Chairman Paul G. Kirk Jr. and Tucker in an attempt to "iron out their differences," according to sources.

Since his election as vice chairman, Burris has sought to consolidate his support among blacks in the DNC. He is trying to arrange a meeting of black DNC members in New Orleans but is running into stiff resistance.

To spur attendance, Burris said he has offered to pay the travel expenses of the black members. That offer, however, has prompted questions about where he is getting money to pay for the meeting, which is not being funded by the DNC.

"It's coming out like I'm trying to bribe people by paying their fare down there," Burris said yesterday. "That is irritating and ridiculous. I said because DNC members are working people and can't fly here and there I would raise money to get them to New Orleans. I said I had some friends who would help to pay the way."

Burris refused to elaborate further.