John D. Ehrlichman, chief domestic adviser to President Richard M. Nixon, has asked President Reagan to pardon his conviction for conspiring to cover up the Watergate scandal, Justice Department officials said yesterday.

Now a writer in Santa Fe, N.M., Ehrlichman, 62, applied for the presidential clemency May 28 and is the subject of an FBI background investigation, according to David C. Stephenson, the Justice Department's pardon attorney.

Stephenson said Ehrlichman has asked for a pardon on the Watergate conspiracy conviction and also his separate conviction for perjury and conspiracy in connection with the break-in by the White House "Plumbers" unit into the Beverly Hills, Calif., office of peace activist Daniel Ellsberg's psychiatrist. Ehrlichman served 18 months in a federal prison.

Even if the examination proves favorable to Ehrlichman, it would not be likely that he would obtain a decision before Reagan leaves office in 17 months if his case is treated routinely, officials said. Pardon applications average 3.3 years to process, reflecting a thorough review and investigation, Stephenson said.

Ehrlichman's plea for forgiveness came to light as some conservative Republicans are pressing Reagan to pardon two key figures in the Iran-contra affair, Marine Lt. Col. Oliver L. North and former national security adviser John M. Poindexter. They have not been charged with any crime but are considered likely targets for indictments that would be sought by Iran-contra independent counsel Lawrence E. Walsh.

During his first term, Reagan denied pardons to two other Watergate principals, Jeb Stuart Magruder and E. Howard Hunt Jr. He did pardon Eugenio Martinez, one of the men who took part in the 1972 burglary of the Democratic Party's offices, whom Stephenson described as "perhaps the least culpable" of the Watergate participants

Ehrlichman, whose convictions led to his being disbarred, has had a successful career as a novelist since his release from prison. Once regarded as among the more dour and rigid of the Watergate conspirators, he seemed to undergo a character metamorphosis, growing a beard and emerging as a relaxed, witty observer of the Washington political scene.

But he has not been able to put his Watergate notoriety completely behind him.

In May, the advertising agency for Dreyer's Grand Ice Cream Inc. in San Francisco dropped Ehrlichman from an ad campaign featuring "unbelievable" people "for an unbelievable product." The Wall Street Journal reported that the ad agency excluded Ehrlichman after about 300 television viewers protested his participation to Dreyer's headquarters.

After the FBI's "full background investigation," which will include interviewing character witnesses he listed on his application, business associates and others who know him, Stephenson will consult prosecutors and the sentencing judges.

Stephenson said he will then prepare a written recommendation that will be routed to the counsel to the president.

The only federal right directly affected by a pardon would be the right to own, transfer and carry firearms, Stephenson said.

The right to vote is regulated by states. New Mexico does not permit convicted felons to vote, but most states would recognize a presidential pardon and restore that right, Stephenson added.