Jesse L. Jackson sharply criticized the Reagan administration's proposed cuts in domestic spending yesterday and unveiled plans for nationwide demonstrations to protest poverty and unemployment, including a prayer vigil across from the White House the weekend before President Reagan's inauguration.

Flanked by Rep. Ron Dellums (D-Calif.), D.C. Mayor Marion Barry and a number of regional labor leaders, Jackson told a gathering at the Shiloh Baptist Church that the proposed fiscal 1986 budget cuts would hurt large numbers of whites, as well as blacks and Hispanics.

"The truth is that most of those who are poor, unemployed, on welfare or some other form of federal assistance programs are white, so there can be no punitive policy that is not ultimately painful to the nation at large," Jackson said.

Jackson, a civil rights leader and unsuccessful Democratic presidential candidate, told reporters he will visit Pope John Paul II next Thursday or Friday to urge an increase in Roman Catholic Church pressure against apartheid in South Africa.

Jackson was granted a visa to visit South Africa Jan. 4-12. However, he said he has asked South African officials to delay his visit until the Feb. 3 installation of this year's Nobel Peace Prize winner, Desmond Tutu, as Anglican bishop of Johannesburg.

He also praised TransAfrica, an organization that has been staging almost daily demonstrations outside the South African Embassy here to protest apartheid.

Jackson called yesterday's session primarily to protest efforts by the Reagan administration to cut domestic spending by $34 billion in fiscal 1986 as part of an effort to reduce the federal deficit.

Barry, president of the U.S. Conference of Black Mayors, said that the District and other major cities would bear the brunt of the proposed cuts and would have difficulty in maintaining or improving their public housing programs.

Jackson announced that he is organizing demonstrations on Jan. 18 in a number of U.S. cities hard hit by unemployment, including Pittsburgh, Chicago and Youngstown, Ohio.

The following day, about 5,000 to 10,000 demonstrators will hold a prayer vigil in Lafayette Square across from the White House to call attention to the problems of unemployment and poverty. Jackson said the demonstration will be staged a day before a private ceremony swearing in President Reagan for a second term and two days before his public inaugural activities.

He said additional cuts must be made in military spending, beyond those already proposed.

In an interview, Jackson insisted that his coalition of progressive blacks, Hispanics, Asian Americans and whites can exert considerable pressure on Congress to block the cuts, despite Reagan's overwhelming reelection victory and the questionable impact of the Rainbow Coalition on congressional and state races.

"Reagan won by a landslide, but we clipped his coattails," Jackson said. "Our drive for justice will outdrive and outlast the fad of Reagan."