Pinch-hitting for President Reagan on a tough assignment, Vice President Bush today assured a skeptical black audience that the Reagan administration would not abandon the federal commitment to "equal justice under law."

In a speech to a Founder's Day observance at Tuskegee Institute, cradle of black education in the South, Bush frankly acknowledged that black Americans are doubtful about the extent of the Reagan administration's commitment to protecting the political, social and economic rights of minorities.

"These doubts just aren't right; they're totally unfounded," Bush said. "President Reagan cares deeply about the lives and livelihoods, the safety and security, of all Americans regardless of race, sex, color or creed."

This declaration as received in silence. But the predominantly black audience warmed up and applauded moments later when Bush repeated the administration commitment to equal justice.

"And we will not tolerate or condone the irresponsible actions of those who would deprive black and minority Americans of their right to life, liberty and the pursuit of happiness, as envisioned by our country's founding fathers," he said.

Bush also was applauded when he promised the Reagan administration would continue to value the role of black colleges and "do what is necessary to assure that the cultural and educational heritage represented by Tuskegee and America's black institutions of higher learning will be preserved and strengthened. . . ."

But there was practically no applause for the central message the vice president brought to Tuskegee, which was the now-familiar Reagan gospel that government spending must be cut back in favor of programs that spring from the private sector.

Borrowing from journalist Simeon Booker the phrase "rhetorical flimflam" to characterize traditional federal spending programs, Bush said the Reagan administration was committed instead to "increased incentives in the private productive sector of our economy and decreased reliance on government remedies that have proved insensitive and ineffective in meeting human needs."

Bush was on relatively friendly ground in making the warning, since Tuskegee is one of the few centers of minority education where federal spending may be expanded during the Reagan administration. The first Job Corps center to be administered directly by an institution of higher learning will open here April 15 under a two-year, $500,000 grant from the Department of Labor.

Bush's trip today was the first taken by the vice president outside Washington since President Reagan was wounded in an assassination attempt March 30. When the trip was planned, it was given important political significance by some Reagan advisers who are concerned that black Americans are the only major group in which the president suffers from a negative job approval rating.

Bush repeatedly assured his hosts today that the president wanted to make the trip but was unable to because he is convalescing from his wound.

The vice president is not considered Reagan's equal as a communicator, and he struggled at times today -- both with sentences he inadvertently dropped from his speech and with his mortar board, which kept slipping from his head.

But Bush saved the day with a series of warm smiles, and he was applauded when he received an honorary doctor of laws degree from Tuskegee president Luther H. Foster, who said, "Yours is the record of unremitting loyalty and energy, placed in the service of this nation."

Bush's role as a presidential substitute will continue through at least two more speeches. He will speak in place of Reagan April 23 at a fund-raiser in Los Angeles, but said he would not substitute for the father of the bride when Maureen Reagan is married in that city the next day.

"I'm not going that far in my standin responsibilities," Bush told reporters on the plan en route to Tuskegee.

He said the day after the Los Angeles speech, he will fly to Hartford, Conn., for another political fund-raiser where Reagan originally was scheduled as the speaker.

The vice president said he expects to continue presiding over some of the Cabinet council meetings in the White House while Reagan is recuperating but that he will gradually phase out of the duties he has been performing while the president was at the hospital.

Reagan's doctors have recommended that he remain in the residence during the coming week and return to part-time duty in the Oval Office the week after next.

"I'll preside at the table to keep things moving until he comes back." Bush said