Top White House and Justice Department aides agreed last night to recommend to President Reagan that he nominate D.C. Court of Appeals Judge Stanley S. Harris to be U.S. attorney for the District of Columbia, a knowledgeable administration source said last night.

Harris candidacy was enthusiastically endorsed during a meeting in the West Wing of the White House yesterday attended by Attorney General William French Smith, White House counselor Edwin Meese III and other key officials who review federal appointments, the source said.

This source said that the White House had received "unanimously favorable reaction" to Harris' potential nomination in contrast to a storm of protest that that erupted three weeks ago when these same aides said they would support New York prosecutor Thomas P. Puccio for the post.

The support for Harris voiced at the White House meeting yesterday seemed to make it clear that Puccio, who came to national prominence when he directed the Abscam bribery prosecutions, was out of contention.

It is expected that Harris' appointment would move quickly through the nomination and Senate confirmation process.

City political leaders had protested that they were left out of the decision making process that generated support for Puccio. Yesterday, D.C. City Council member David A. Clarke, who had lead the council opposition to Puccio, said that "we weren't consulted this time either. Nevertheless, (Harris) is much better than . . . Puccio."

Another high ranking city official said yesterday that "some people at the White House may have talked to some of their friends in the Washington community. But so far as I know they have not discussed this matter with the leadership of the Washington community."

Washington lawyers who had complained about choosing a U.S. attorney from outside the nation's capital lauded Harris, a native Washingtonian, not only for his capabilities as a lawyer but for his willingness to leave the security of the appellate bench and take over the prosecutor's office.

Harris declined to comment yesterday.