After a week of criticism about distancing himself from the Republican Party, Mayor Bloomberg seems to be reminding his base that he is still the GOP candidate.

Last night, as President Bush attended inaugural balls to ring in his second term, Mr. Bloomberg, who chose to skip the Washington festivities, addressed the New York Young Republican Club in Midtown.

“Look,” he told the well-dressed crowd of professionals, “there are three things we all believe in: America, the city of opportunity, and the hope that Howard Dean becomes the head of the DNC.”

The crowd laughed at Mr. Bloomberg’s joke about installing the failed presidential contender as chairman of the Democratic National Committee, but the mayor may have a harder time winning enthusiastic support for his re-election from the rest of his party.

A former Republican member of the City Council, Thomas Ognibene, announced this week that he would challenge the mayor in a primary. He said he was responding to conservatives in the city who feel that Mr. Bloomberg used the party to get elected and then forgot about Republican concerns.

“There is no question that his is trying to repair his relationship with the party,” Mr. Ognibene said yesterday. “He distanced himself from the Republican council members and he treated them disrespectfully. I happen to know now that his people are running in circles trying to repair that damage.

“I know he is reaching out to at least the Queens Republican Party, even though he hasn’t made a phone call to the party in three years,” Mr. Ognibene continued.

The line is a fine one for Mr. Bloomberg. He needs to maximize his conservative votes to win November’s election, yet he can’t come across as too conservative in a city where Democrats greatly outnumber Republicans.

Across town last night, the speaker of the council, Gifford Miller, was raising money to challenge Mr. Bloomberg and seeking to link the mayor with the very conservatives that Mr. Ognibene says the mayor has alienated.

While Mr. Bloomberg took heat for the alleged indiscriminate arrests of protesters during the Republican National Convention over the summer, he used the convention to connect with the crowd last night. The visibility and advertising the city got from the event and from “treating protesters fairly” will help the city for years, he said.

“I’ll try to get the Republican convention to come back, and I’ll try to get the Democratic convention to come here,” the mayor said.

The president of the young Republicans, Dennis Cariello, disputed the notion that Mr. Bloomberg failed the party. He has donated money to GOP causes, appeared at GOP events, and guided the city through a rocky fiscal period, Mr. Cariello said after the mayor left.