As Mayor Bloomberg was walking into a Juniper Park Civic Association meeting Thursday night in Queens he spotted Council Member James Oddo in the parking lot and stopped to shake his hand.

Under different circumstances, a friendly encounter in a city full of Democrats between two Republicans who work in the same building would probably not have been worthy of even a footnote. It would have been business as usual.

But as the council’s Republican minority leader, Mr. Oddo has had an unusually rocky relationship with Mr. Bloomberg that dates back to 2003, when he stormed out of a Gracie Mansion dinner to protest the mayor’s 18.5% property tax hike.

Yesterday, the two men put their lingering differences aside when Mr. Bloomberg signed into law a bill the Staten Island council member introduced in 2001 to require portable defibrillators in facilities ranging from municipal buildings to large private health clubs.

During a bill-signing ceremony at City Hall, Mr. Oddo, thanked the mayor – and made a reference to the strains in their relations. “Sometimes you bump heads with some very important people … but there are days like this that make it rewarding and remind you why you got into this line of work to begin with,” he said.

For his part, Mr. Bloomberg said his company, Bloomberg LLP, has installed the notebook-sized devices in its offices all over the world. The mayor said he even had one at home.

About an hour before the ceremony, however, Mr. Oddo said while he has seen more action for his district in the months since he turned up criticism of the mayor, there is still a long way to go. Asked whether there had been any thawing in connection with the defibrillator bill, he said: “It’s governmental. I’ll be cordial to the mayor and I’m sure he’ll be cordial to me. But in terms of helping the relationship, the relationship needs a lot more than just sitting next to each other signing a bill.”

The council member also pointed out that the administration had initially protested parts of the bill and that the final version was very much a compromise.

Mr. Oddo, who has not yet endorsed anyone in the upcoming mayoral race, also has a close relationship with his predecessor as council GOP leader, Thomas Ognibene, who plans to challenge the mayor in a Republican primary. Mr. Oddo said yesterday there was no point in making an endorsement this early.

Though the mayor has the backing of other prominent Republicans on Staten Island, including a former borough president, Guy Molinari, the borough, which gave Mr. Bloomberg more than 70% of its votes in 2001, is seen as vital to the mayor’s re-election. And this time, political analysts have said, garnering that level of support is not going to be easy.

The mayor’s communications director, Bill Cunningham said: “The mayor has probably been to Staten Island more than any other mayor each and every year he’s been in office.” He also said the administration is doing nothing different in the borough now, it’s simply that longtime projects are now beginning “to pop.”

“If there’s a momentary lapse in a relationship with anybody,” he said, “that is not going to get in the way of us working with the local elected officials and the community groups to take care of the needs of the people on Staten Island.”

Mr. Oddo said he, too, is focused on government, because “there’s been a lot of blood-spill political side.” His plan is to reconsider his endorsement as the election gets closer and he sees how the relationship unfolds. Late in the day, after the bill-signing, Mr. Oddo issued a news release attacking the administration for not providing funds for staff at a newly built firehouse at Staten Island’s South Shore.