The end of the election season often ushers in a cooling-off period between political opponents.

Such a thaw was on display yesterday, when Mayor Bloomberg and the head of the most powerful health care union in the state, Dennis Rivera, stood together to promote a tax credit for poor working New Yorkers.

Mr. Rivera, who endorsed Mr. Bloomberg’s Democratic opponent in the last election and publicly chided the mayor during the campaign, called the credit “God’s blessing” and commended the administration for promoting it aggressively.

The refund is available to families and individuals that meet certain income eligibility requirements. A family making about $33,000 that has more than one child, for example, could be eligible for as much as $5,940 from the federal, state, and city government.

Mr. Bloomberg said the refund would put more money into the pockets of working city residents and in turn pump $1.5 billion into the local economy.

The mayor also announced the opening of 40 free tax preparation centers and said the city has entered partnerships with 100 nonprofit and private organizations in an effort to get eligible New Yorkers to file for their earned income tax credit. In addition, H&R Block and Jackson Hewitt, two tax preparation companies, will be offering discounts to six labor unions, including Local 1199, and eligible families that are new customers.

“If you don’t make a lot of money, you can get some money back here,” Mr. Bloomberg said at one of the tax preparation sites in Harlem.

The program highlights just how much the tide has turned since Mr. Bloomberg trounced Mr. Ferrer to win a second term.

When Mr. Rivera endorsed Mr. Ferrer in September, he accused the mayor of trying to dampen the endorsement by suggesting that Local 1199 had offered to back the mayor in exchange for putting 25,000 home health aides on the public pay roll. The implication was that there was a quid pro quo arrangement and that the union’s endorsement was for sale.

“We don’t get mad, we get even,” Mr. Rivera, told a crowd of cheering union members at the time.

After the Bloomberg announcement yesterday, Mr. Rivera played down the rift.

“We’re very happy with the state of our relationship with the Bloomberg administration,” he said. He said he was never “angry” with the mayor and indicated that the situation was blown out of proportion.

A spokesman for the mayor, Stuart Loeser, said Local 1199 is an “important partner” in the earned income tax credit program and many other projects.

“We’ve been working with him, we’re going to continue working with him,” Mr. Loeser said of Mr. Rivera. “The endorsement has no effect on projects like this.”

The city is distributing materials about the tax credit in 11 languages. Last year, 800,000 filed for the credit, but about 200,000 eligible residents failed to.

Mr. Bloomberg, who is a billionaire, said he is not eligible for the program, but joked that the Federal Insurance Contributions Act deductions cut his $1 annual mayoral salary to 93 cents.