The new president of the National Urban League said yesterday that the Reagan administration's "savage" budget cuts and its "betrayal of basic civil rights protections" have left black Americans with the feeling of being under siege.

John E. Jacob, who took over the leadership of the Urban League Jan. 1, singled out the administration's decision to prohibit the Internal Revenue Service from denying tax exemptions to schools that discriminate as its most "unconscionable" act. And the president's "fast backtracking," by announcing later that he would propose legislation to bar the tax exemptions, did not repair the damage, Jacob said. Profile on Page D1

"The administration's claim that this is simply a procedural issue about legal authority does not hold water," Jacob said. "Its actions provided aid and comfort to the racists in our midst. Taken together, these and other steps can only be interpreted as attempts to dismantle the process of desegregating America."

Saying that it has been years since blacks have felt so "vulnerable" and "alienated from their government," Jacob insisted that Reagan order his Justice Department to "call a cease-fire in its war on affirmative action," and he urged congressional leaders to tell the White House that further cuts in programs aiding the poor are unacceptable.

Jacob's blast at the Reagan administration came at a press conference at Howard University to announce the release of the League's annual "State of Black America," a compendium of scholarly analyses on the status of blacks in such areas as economics, education, affirmative action, and politics.

The speech by Jacob, who succeeded Vernon Jordan as head of the League, seemed to signal that he, like Jordan, sees a major part of his duties as being a highly visible spokesman for black concerns.

He appeared defensive about criticism that civil rights groups have not made enough effort to mobilize the black community in recent years. He said the League plans a voter registration campaign before the 1982 elections, but said community mobilization is a job not only for civil rights groups "but for every community organization and every individual."

Jacob described no new League strategy in its rearguard battles with the administration. He spoke generally of the need to build coalitions of groups concerned with the "terrible pressures placed on poor people," but he did not detail how this might be accomplished. His hopes seemed to be pinned on what he described as a sense that a "new realism" in opposition to further budget cuts was emerging among congressmen who "recognize the political risks involved in policies that put their constituents out of work, increase pressures on local governments in their districts and outrage the moral sensibilities of Americans who believe in fairness."

One of the key tests of such a "new realism," Jacob said, will be Senate action on the Voting Rights Act. He called for swift passage of the bill that passed the House and urged Reagan to abandon his opposition to that legislation.