A disagreement over how to pay for a September 11th counseling program, already the source of a clash between Senator Clinton and Governor Pataki, is now bubbling over at City Hall.

City Council Speaker Gifford Miller, a likely 2005 mayoral candidate, attacked Mr. Pataki and Mayor Bloomberg yesterday for turning away $4.5 million from the Federal Emergency Management Agency. The money would extend the counseling program called Project Liberty to fire fighters, police officers, and their families.

“All he has to do to get $4.5 million for the state and city of New York,” Mr. Miller said, speaking of the governor, “is just ask. That’s it. All he has to do is ask. This money is ours.”

Mr. Pataki has said the funds, which were secured by Senator Clinton, would be better spent on other programs. He has instead proposed having the city pay $2.5 million and the state $2 million to extend Project Liberty.

The Bloomberg administration, which had originally backed Mrs. Clinton’s efforts, changed its stance. It said that it is already competing for scarce FEMA dollars for other purposes and that it makes more sense for the city to kick in its share, to avoid competing with itself for the remaining federal money.

The mayor’s chief spokesman, Edward Skyler, said yesterday that the city already has outstanding FEMA requests and that adding Project Liberty to the wish list would delay approval for anything. Contrary to Mr. Miller’s statement, he also said the $4.5 million would be reimbursing the city for dollars it already dished out.

“It’s an accounting thing,” Mr. Skyler, the mayor’s press secretary, said. “It’s quicker and easier for the city and the state to pay for it.”

Though $2 million barely registers as a blip in the city’s budget of well over $40 billion, Mr. Miller and a fellow Manhattan Democrat on the City Council, Margarita Lopez, who joined him at a news conference yesterday, said it was unacceptable for the Bloomberg administration to cry poverty during budget negotiations and then reach for its checkbook to resolve this matter.

They accused Mr. Pataki of stonewalling on the deal to appease his GOP counterparts and nullify the accomplishment of Mrs. Clinton – a Democrat. A spokesman from Mr. Pataki’s office put the blame on Mr. Miller, accusing him of playing politics.

The tug-o’-war over a program that both sides want financed may seem like insider baseball, but council members argue that turning down what they say is pre-allocated funding will increase the city’s tax burden and send the wrong message to the federal government about the needs here.