Mayor Bloomberg has changed course and decided not to veto a bill that will increase the amount of money labor unions can donate to candidates running for office.

The mayor had a deadline of today to reject the measure officially, but his staff confirmed late yesterday afternoon that he decided to back down from his plan to do so.

As a result, the bill, which has been at the center of an unusually intense debate, will quietly become law next month.

“The Mayor will allow the legislation to lapse into law because he doesn’t see the point of vetoing a bill he agrees with conceptually, especially since it would be over-ridden,” his spokesman, Edward Skyler, said in a statement sent by e-mail. “His objection has always been to the City Council changing the rules in such a self-serving manner.”

The legislation changes the definition of what counts as a single entity or “single source” under the city’s campaign finance law. Under current law, an entity can contribute no more than $2,750 to a candidate for City Council and $4,950 to someone running for mayor or another citywide office.

In an attempt to clarify its rule this spring, however, the Campaign Finance Board said affiliates of the same parent organization must count as one entity unless they prove they are separate. The idea, the CFB said, was to prevent candidates from flouting contribution limits.

The move angered council members, who rely heavily on donations from unions to run for office, and the unions, which wield influence over legislation through donations.

Both argued that most affiliates operate independently and should be considered separate because they have different voices and views. The example most commonly cited is Local 1199, the massive health care workers union, and 32BJ,the building workers union. The affiliates fall under the same of the Service Employees International Union, but are so independent that they endorsed different candidates in the mayoral election. The council’s bill does outline four criteria that affiliates must meet to be considered separate, but critics viewed them as token measures.

In addition to his own statement Mr. Skyler emailed a transcript of comments Mr. Bloomberg made last month when he said smaller unions should have the right to support different candidates. “I think that each individual local union should be able to give away money to whomever they want and not be restricted by what another part of the amalgamation or conglomeration of unions does,” Mr. Bloomberg said. The mayor added, however, that the decision should be up the Campaign Finance Board. Allowing a council whose members benefit from the change to act in their own self interest undermines “the credibility of our whole Democratic process,” the mayor said.

In October, Council Member Annabel Palma, a former 1199 worker, filed a lawsuit against the Campaign Finance Board challenging the constitutionally of the “single source” rule and another regulation. She argued it was a First Amendment violation to restrict donations that helped her get her message out. Those who have been watching the situation unfold said they were surprised the mayor was opting not to veto, considering that his office said otherwise as recently as last month.

The president of Citizen’s Union, Dick Dadey – whose organization favors allowing unions to make individual donations, but viewed the council bill as too permissive – said the mayor’s decision broke with past practice.

“It’s puzzling because this is essentially a flawed bill that has loopholes,” Mr. Dadey said.

“One could argue that the mayor is responding to the concerns of a constituency group that supported him for reelection,” Mr. Dadey said. “There is nothing inherently bad about that. It just seems to be a departure from his past practice.”

The senior attorney for the New York Public Interest Research Group, Gene Russianoff, said it was a “crummy bill” and said the mayor was probably told by his staff that it was “a sinker.”

When asked whether he thought Mr. Bloomberg backed off in a nod to the unions that endorsed his bid for reelection, Mr. Russianoff said: “It doesn’t hurt the mayor to do what the unions want. Is he returning the favor to the unions? It doesn’t hurt him and it probably helps him.” The mayor’s staff denied that it was any kind of giveback. A senior fellow at the Manhattan Institute, Steven Malanga, said he thought the mayor was picking his battles because he knows that the heavily Democratic council can override his veto.

“We now have such a solid Democratic majority in the City Council that is so completely in the pocket of the unions that they can pass any legislation and override the mayor’s veto on virtually any labor legislation,” Mr. Malanga said.

The chairman of the Campaign Finance Board, Frederick A.O. Schwarz Jr., said in a statement yesterday: “The Board is very disappointed and does not believe that the Administration has fully appreciated the ramifications.”

Several of the bill’s strongest supporters are in the running to replace Gifford Miller as the next speaker of the council.