The Rev. Jesse L. Jackson, saying he was entering late because he "had to start from further back" and playing down his lack of support from many black elected officials, announced on television last night that he will seek the Democratic nomination for president.

Jackson, who had been considering the decision for more than a month, had said last week that he would make his announcement on Thursday at the Washington Convention Center.

Instead, he used an interview on CBS's highly rated "60 Minutes" news program as his forum.

Jackson told interviewer Mike Wallace that he is seeking the nomination because of his concern that too much of America's greatness has been measured in bombs, slavery, broken treaties and abuses of power.

"You measure America's greatness by what America does for the least" of its people, he said. "I want to help again measure greatness by how we treat children in the dawn of life, how we treat poor people in the pit of life and how we treat old folk in the sunset of life. That's the America I want to identify with."

Later last night, Jackson told a college audience in Atlanta that on Thursday he will become an official candidate in the Democratic primaries.

A civil rights leader and national president of the Chicago-based Operation PUSH (People United to Serve Humanity), Jackson, 42, has never held elective office, a source of criticism from many who opposed to his entering the race.

However, Jackson said that, having traveled to Africa and the Middle East, he has broader experience in foreign policy than President Reagan did when he took office.

Jackson said the field of seven white males seeking the Democratic nomination is not representative of minorities. He also said that despite lack of support by many black politicians and civil rights leaders for his prospective candidacy, he can win votes on "the open market."

Jackson also said that if he had been president he would not have invaded Grenada and would not have sent troops to Beirut. He repeated his assertion that more nuclear missiles should not be deployed in Europe and that Reagan should instead seek a summit meeting with Soviet leader Yuri V. Andropov.

Like the other Democratic candidates, Jackson said he will consider a woman as a running mate and will choose one if he can.

Asked if he considers it a contradiction of his self-styled grass-roots political philosophy that one of his children attends the exclusive St. Albans School here, Jackson said no.

"I've always fought for the options of American education, but I would never fight for tuition tax credits," he said. "I have five children . . . and they require different things."