D.C. Republicans claimed victory yesterday for President Reagan in his debate with Walter F. Mondale Sunday and predicted that Reagan would double his showing of four years ago in the heavily Democratic District.

"He Reagan was in command of the issues, comfortable with the facts and made effective use of humor putting the age issue to rest once and for all," said Clarence McKee, chairman of the D.C. Reagan-Bush campaign committee.

At a news conference at the committee headquarters near the White House, McKee predicted that Reagan would win 25 percent of the votes cast in the District Nov. 6, primarily with the help of "a lot of closet Republicans" and blacks satisfied with the president's economic program.

In 1980, challenger Reagan picked up only 13.4 percent of the D.C. vote while rolling to a massive victory nationwide over Democratic President Jimmy Carter. Reagan received 23,545 votes in the District compared to 131,113 for Carter.

Mayor Marion Barry, a cochairman of the D.C. Mondale-Ferraro campaign, said yesterday that Mondale did extremely well in attacking Reagan's foreign policy and questioning his leadership ability. However, Barry conceded Mondale did not deliver a decisive blow.

"When these debates happen, in the minds of the public it's like a heavyweight championship fight," said Barry, who attended the debate in Kansas City. "The benefit of the doubt goes with the champion. And people view Mondale as the challenger and Reagan as a champion."

D.C. City Council member Charlene Drew Jarvis (D-Ward 4), a Mondale supporter who also attended the debate, saw it differently, arguing that the outcome was "a real plus" for Mondale.

"Mondale won on substance, he won on debate technique, and he lost on acting," said Jarvis, a national cochairwoman of the Mondale-Ferraro campaign. "I think the fact that he was so strong in the second debate means people who already decided for Reagan will consider switching and those who were undecided will move affirmatively for Mondale."

Jarvis and Barry agreed that, despite Republican claims to the contrary, Reagan failed to dispel completely doubts about his age and his acumen as a leader. They cited Reagan's fuzzy or erroneous responses to some questions and his rambling four-minute summary, in which he recalled trying to collect his thoughts while driving along the California coast several years ago.

"At the end, I thought he was going to finally get to Santa Barbara," Barry said.

Not surprisingly, D.C. Republicans saw it differently, arguing that Reagan made a strong showing and put Mondale on the defensive because of his votes against defense spending while he served as a U.S. senator from Minnesota.