The White House said yesterday that Richard V. Allen must pass a new test before returning as the president's national security adviser: a review by the presidential counsel's office to see if White House "regulations" were violated, regardless of whether Allen is fully exonerated by the Justice Department.

White House deputy press secretary Larry Speakes said this review will not begin until after the Justice Department completes its investigation of unanswered questions in the Allen case. The department said Tuesday that Allen violated no laws in receiving $1,000 from Japanese journalists that was intended as an honorarium for their interview with Nancy Reagan. But the department is still investigating Allen's acceptance of two watches, given him by either a Japanese friend or Japanese journalists who interviewed Mrs. Reagan, and errors in his financial disclosure statement.

Speakes' statement was the most complete White House declaration of hurdles Allen must clear to return to his job. For a time yesterday, the matter seemed far from clear as presidential advisers compounded confusion by issuing conflicting comments about the affair.

Presidential counselor Edwin Meese III, Allen's strongest defender within President Reagan's hierarchy, was asked while walking into a Washington hotel if he expects Allen to return if fully cleared by the Justice Department.

"I certainly would think so, sure," Meese said, making no mention of a White House counsel's review. "I would see no reason why he shouldn't come back after this is all cleared up." This seemed to contradict the version Speakes offered in his daily news briefing. In late afternoon, Speakes said that his statement was indeed accurate and that Meese must have forgotten about the additional review to see whether White House regulations had been violated.

Mrs. Reagan, chief of staff James A. Baker III and his deputy, Michael K. Deaver, reportedly have urged that Allen be replaced for exercising bad judgment, even if he violated no laws.

After the Justice Department issues its final report, Speakes said, the office of White House counsel Fred Fielding "will review and make a recommendation as to whether any White House regulations were violated." He said Fielding will not personally be involved since he is a close friend of Allen and served as Allen's attorney when Allen was a business consultant prior to President Reagan's inauguration.

Allen's fate may rest on whether his White House colleagues believe his explanation that he received both watches before taking his White House job Jan. 20 and that they were given to him by an old friend, Mrs. Chizuko Tasake. The other version is that of Japanese journalist Fuyuko Kamisaka, who interviewed Mrs. Reagan.

Kamisaka has said she bought a gold watch and a silver watch, valued together at about $340. The gold watch was left at Allen's office Jan. 16, four days before the inauguration.

When the interview with Mrs. Reagan was concluded one day after the inauguration, she said, Allen was asked if he liked the gold watch or preferred the silver one. Allen said he would keep the gold watch and take the silver one, Kamisaka has said.

A White House official said the counsel's review will determine whether Allen violated either of two regulations: the "White House Standards of Conduct" or an executive order concerning receipt of gifts.

The official said the standards regulation provides that White House officials may not receive gifts valued at more than $35 or totaling more than $100 from any one source other than a relative.

Section 201 (a) of Executive Order 11222 says that "no employe shall . . . accept directly or indirectly any gift . . . of monetary value from any person . . . who is seeking to obtain . . . business . . .relationships with his agency . . . or has interests which may be substantially affected by the performance or nonperformance of his official duty."