President Reagan sought to shore up his base among "social-issue" conservatives yesterday by pledging unremitting support for constitutional amendments that would ban abortion and permit school prayer.

On the day he submitted to Congress a budget that has brought him criticism from some economic conservatives the president went before a convention of religious broadcasters here to reaffirm in emotional terms his commitment to these amendments and tuition tax credits.

"Let us come together, Christians and Jews, let us pray together, march, lobby and mobilize every force we have, so we can end the tragic taking of unborn children's lives," Reagan said on behalf of the anti-abortion amendment.

Speaking of the school-prayer amendment, which failed last year in Congress, Reagan said, "I am determined to bring back that amendment again, and again, and again, until we succeed in restoring religious freedom in the United States."

This rhetoric was a staple of Reagan speeches in the 1970s, as was another oft-used line that the president quoted yesterday: "The American people . . . are hungry for a spiritual revival."

Although the rhetoric was not new, its use yesterday served a timely political purpose. Conservative publications and spokesmen have become increasingly critical of the administration in recent weeks, questioning whether the White House has abandoned conservative principles and whether the president is a captive of his staff.

At the same time Reagan has modified his economic views by proposing a contingency tax increase and a slight slowdown in the pace of military spending, he has sought to reassure his basic constituencies that he has not changed his principles.

In his speech yesterday Reagan urged Americans to read the Bible and teach religious values. His speech, studded with biblical citations, quoted Jesus, John Adams, Benjamin Franklin, British critic Malcolm Muggeridge and Russian writer Alexander Herzen on behalf of the proposition that spiritual values will triumph over material ones.

" . . . When I hear the First Amendment used today as a reason to keep moral values away from policy-making, I am shocked," Reagan said. "The First Amendment was not written to protect the people and their laws from religious values; it was written to protect those values from religious tyranny."

The president's most emotional language was reserved for the abortion issue. "Who among us can imagine the excruciating pain the unborn must feel as their lives are snuffed away?" Reagan said. "And we know medically they do feel pain."

Reagan was applauded loudly at the National Religious Broadcasters convention for his remarks on the prayer and abortion issues and also when he renewed his appeal for tuition tax credits, which would benefit parents who send children to parochial and other private schools.

The tax-credit proposal was rejected in the last Congress, but Reagan said that soon "we will begin the struggle all over again to secure tuition tax credits for deserving families."

While the president was renewing the struggle on social issues, White House chief of staff James A. Baker III was attempting to improve White House management procedures.

Baker named John S. Herrington, assistant secretary of the Navy for manpower, as a 60-day consultant to make a study of the press, public liaison, intergovernmental relations and political operations.

"It's impossible for me, sitting here, to know which offices are operating efficiently from a managerial standpoint," Baker said.

"I'm constantly hit with competing demands for staff and other resources. I need a management expert to tell me where these scarce resources should be allocated."

Herrington, 42, performed a similar role in 1981 as a troubleshooter in the White House personnel office when its operations were being criticized severely from several quarters.