Loretta Cornelius, deputy director of the Office of Personnel Management, yesterday continued to ignore intense pressure from the White House to quit voluntarily before President Reagan fires her.

White House spokesman Albert Brashear, breaking with tradition by commenting on the record about a pending personnel matter, yesterday said: "We have already contacted her and informed her that we think a resignation is in order, in light of the fact that we think all Cabinet members have the right to pick their own deputy directors."

He said, "At this point in time, we have made it clear to her that we would like her to resign," adding that Cornelius was given no deadline for resigning and that Reagan had not yet become personally involved in this unusual case.

Cornelius was out of town and unavailable for comment. Her lawyer, Joseph Petrillo, said Cornelius had not resigned despite the repeated and public White House warnings, and the unusual stalemate continued. Cornelius believes that only the president, and not his subordinates on the White House staff, can ask her to leave, Petrillo said.

The White House has wanted Cornelius to resign since June, when her testimony before a Senate committee torpedoed the renomination of her boss, former OPM director Donald J. Devine, a favorite of conservatives. Last week, White House officials for the first time told Cornelius directly to hand in a letter of resignation. This week the administration began mounting a public campaign to turn up the pressure against her.

An OPM spokesman said that now "it's up to the White House to do something," since the new director, Constance Horner, has no power to fire Cornelius.