The Federal Communications Commission reluctantly agreed yesterday to consider at least one downtown Washington office building before signing contracts to move the agency's 1,600 employes out of the city and into two Rosslyn high-rise buildings.

Acting FCC Chairman Robert E. Lee told members of the House District Committee that, at the request of the committee, his agency will delay signing a lease for up to 20 floors in Rosslyn's Twin Towers until it has considered a proposal from Washington developer Raymond C. Brophy.

Brophy, who is constructing an 11-story office building at 450 5th St. NW on Judiciary Square, told the committee he could provide nicer, more convenient space at a price comparable to the $17.03 a square foot the FCC expects to pay in Arlington's 30-story Twin Towers.

Brophy said he had written the FCC 10 times since last fall seeking information on how his firm could make its offer, but that none of his letters had been answered. He said if a dozen of his questions were answered, he could make an offer to the FCC within 48 hours.

Abbott Washburn, the only FCC commissioner to vote against Moving the agency, has accused the FCC staff of purposely ignoring possible downtown sites because they secretly had decided to move to Virginia more than a year ago. Outgoing FCC chairman Charles Ferris said the staff worked on the Rosslyn move for nine months last year before commission members were informed of their actions, said Washburn. "I read about it first in The Washington Post."

He told the committee yesterday "There has been deliberate blindness . . . [the staff] has failed to make an honest effort to study alternatives."

Acting Chairman Lee said the FCC made an 11th-hour effort in December to see if comparably priced office space was available in downtown Washington. The FCC even puts ads in the newspapers, but no comparable offers were made, he said.

"We have a bird in hand [in Rosslyn]. The other proposals are in the bush," Lee told Del. Walter E. Fauntroy (D-D.C.), who chaired the hearings. Fauntroy accused the FCC of attempting to pull off "an unarmed coup d'etat . . . a sudden exercise of political force by a small, fast-talking group" who are ignoring the opposition of groups that deal with the FCC and the preference of its 1,600 employes to stay in the District.

The FCC claims it must move because leases soon will expire on the five Washington buildings where its employes work. But Fauntroy argued that the first lease won't expire until May 1982, and that affects only 100 employes. They could easily be absorbed at other FCC offices, he said, because the agency is being reduced by the Reagan administration.

The FCC expects its present Washington staff to drop to 1,670 to no more than 1,580 next year, and its space needs to be reduced from the 425,000 square feet it sought last year to 375,000-390,000 square feet.