The Justice Department closed out its investigation of national security affairs adviser Richard V. Allen yesterday saying it had found no need to request a special prosecutor. But there were no assurances from the White House that Allen will be allowed to return to his job.

A statement released at the White House said, "The president is pleased that the Department of Justice has concluded that no special prosecutor should be appointed. Some other issues concerning White House regulations and procedures have been raised which are beyond the purview of the Department of Justice inquiry.

"An internal inquiry conducted by legal counsel Richard Hauser is proceeding on these questions. The White House will have no further comment until that inquiry has been completed."

Allen said yesterday that he expects to return to work "shortly."

Questioned by reporters outside his Arlington home, he said he was confident that he will be cleared in the matters under investigation by the White House just as he was on those studied by Justice. "Whatever they are, they will come out precisely the same way as the previous two matters," he said.

"These matters have been laid, by and large and in great detail, to rest," he went on. "My judgment was quite good. I think my memory can be faulted. I think this entire matter was rife with innuendo and rumor."

But he added, speaking for his family, "We don't feel we've been victimized in any way," and said, "I've never been disappointed in President Reagan."

The Justice Department inquiry that ended yesterday had focused on Allen's acceptance of gifts of wristwatches from a former Japanese business associate and his wife, and on inaccuracies in financial disclosure forms he submitted on taking office.

On Dec. 1, after a separate inquiry, Allen was cleared by the Justice Department of any wrongdoing in connection with his receipt of a $1,000 gratuity from Japanese journalists who had an interview with Nancy Reagan early this year. The money was found months later in a locked file cabinet, and Allen said he had forgotten to turn it over to the government as he had intended.

Allen, who helped set up the interview at the request of Mrs. Tomotsu Takase, has been on paid administrative leave since Nov. 29, when he announced that he was stepping down pending completion of the Justice Department investigations.

On the question of the gifts, the inquiry revealed that Allen received three Seiko watches rather than the two originally reported. He revealed the existence of the third watch Nov. 29 in response to questioning by the FBI.

The report left up in the air one question in the case, which was whether Allen received any of them after he became an official of the government. Public officials may not accept anything of value in return for the performance of any official act.

FBI interviews with participants in the exchange indicated that before the inauguration he received one men's Seiko watch from Tomotsu Takase, a long-time friend and business associate, and a women's Seiko from Mrs. Takase.

The accounts of witnesses differed on whether Allen received the third watch from Mrs. Takase before or after Mrs. Reagan's Inauguration Day interview with Shufu No Tomo (Friend of the Housewife).

In a report to the U.S. Court of Appeals here, Attorney General William French Smith said, "There was no basis for concluding that Allen accepted the watches with the knowledge that they were given to him to influence or thank him for performing an official act.

"Even viewing the facts in the worst possible light, they do not present evidence of criminal intent. In order for Mr. Allen to have violated the law , he would have to have known that the watches were given to thank him for an official act or to influence him in an official act," Smith said.

"To the contrary . . . based upon Allen's long and close friendship with the Takases, Allen could have reasonably believed that the watches were personal gifts to him and his wife," he said.

Smith concluded, "I hereby notify the court that I find this matter to be so unsubstantial that further investigation or prosecution is unwarranted and that no special prosecutor should be appointed for this matter."

Under a 1978 law, a special prosecutor must be appointed to conduct an investigation if a preliminary review by the Justice Department turns up any substantial evidence that a high-ranking government official may have committed a federal crime.

Smith dealt with Allen's financial statement in a separate report that was not sent to the court. The financial statement came into question after it was disclosed that Allen had improperly listed the date of sale of his former consulting firm, Potomac International Corp., to former Reagan aide Peter Hannaford as 1978 when it was actually sold last January.

He later filed an amended, corrected version of the statement.

The inquiry found that there were "inadvertent" and "innocuous" errors on the form involving the date and the terms of the sale to Hannaford, but said they did not violate the law because Allen's misstatements were not "knowing and willful."

"There are enough non-material, obviously inadvertent errors to make credible Mr. Allen's assertion that more material errors were the product of confusion or inadvertence," the department report said.

"While it is clear that Mr. Allen did not exhibit as much care as hindsight would suggest in completing the form, there is no basis to conclude that there were any knowing and willful falsifications."

Besides misstating the date of sale for his company, Allen failed to list the names of former business clients who paid him more than $5,000 in fees as required by the White House financial disclosure regulations.

Federal officials are required to list clients because they could pose potential conflicts of interest.

Allen had a number of Japanese businesses as clients before taking his White House post, and has met with several of them since January, but he has said he maintained an arms-length relationship on policy-making that might affect his former clients.

Allen has said he was advised by the White House counsel's office that, although he was president and sole shareholder of Potomac International Corp., he was technically just an employe of the corporation and therefore not required to list clients on his disclosure form.

Attorneys in the White House counsel's office told FBI investigators that they had no recollection of such a conversation, but the Justice Department found that the legal reasoning was sound.

"The advice appears on its face to be a reasonable and justifiable interpretation of the financial disclosure instructions," the report said.

The attorney general concluded that Allen's violations of the financial disclosure rules were so minor there was no need even to make a report to the appeals court, as had to be done in the case of the watches.