Mayor Bloomberg may have showered Senator Lieberman with praise when he was helping the maverick eke out a re-election victory in November, but his relationship with the Connecticut lawmaker seemed anything but chummy yesterday.

In a letter to Mr. Lieberman, Mr. Bloomberg called the homeland security legislation the senator sponsored a “deeply flawed bill” that would represent a “major step backward” and “make America less secure, not more.”

“The Improving America’s Security Act of 2007 will do anything but,” the mayor wrote to Mr. Lieberman, the chairman of the Senate Homeland Security and Governmental Affairs Committee.

“This bill cuts risk-based counterterrorism funding in favor of politically popular allocation criteria that will further diminish and dilute the effectiveness of federal investments in counterterrorism,” Mr. Bloomberg wrote in the letter, which was also addressed to the ranking Republican on the committee, Senator Collins of Maine.

The tone of the letter represents a departure from the mayor’s enthusiastic backing of Mr. Lieberman on the campaign trail, when he appeared with the senator at the Stamford train station to stump with morning commuters.

The mayor also held several fund-raisers for the lawmaker and even dispatched several of his own staffers to work for the Lieberman campaign.

While some have considered Messrs. Bloomberg and Lieberman political soul mates, Mr. Lieberman’s powerful position as head of the Homeland Security Committee does not seem as if it will bear funding fruit for New York. Although Mr. Bloomberg has repeatedly testified that New York should get more money because it is a terrorist target, Mr. Lieberman has favored a formula that gives a certain amount of money to all states, including small ones like Connecticut.

At issue is the implementation of the recommendations of the September 11 commission. The Senate bill calls for all states to receive an automatic .45% of homeland security funding, which opponents say is too much. The House version calls for states to get .25%, leaving more to be allocated by risk.

A spokesman for Mr. Bloomberg, Stuart Loeser, said the two lawmakers did not discuss homeland security funding during the campaign.

“The mayor respects Joe Lieberman because he does what he thinks is right, just like the mayor does. They disagree on this issue, and he is going to keep pressing Congress on this issue,” Mr. Loeser said. “This is not a partisan issue. It’s urban versus rural. It’s big state versus small state.”

In an e-mail message, a spokeswoman for the Senate Homeland Security Committee, Leslie Phillips, defended the bill, calling it a “fair compromise proposal” and saying the measure will actually increase funding for terrorism grants by 31%, to $2.19 billion. City officials dispute those numbers, saying they are preliminary authorization figures and do not represent realistic appropriations.

Ms. Phillips said the bill would increase funding targeted specifically for high-threat cities by 66%, through an urban initiative. Mr. Bloomberg noted, however, that the number of cities eligible for grants has risen to 100 from 46.

Political analysts saw Mr. Lieberman’s re-election as a political win for Mr. Bloomberg. If Mr. Bloomberg opts to run for president in 2008 as a third-party candidate, the support of established independents such as Mr. Lieberman will be invaluable.

Rep. Anthony Weiner, a Democrat who is planning on running for mayor in 2009, noted, however, that Mr. Lieberman has not changed his position on homeland security funding.

“This is the same position Joe Lieberman had when Mayor Bloomberg campaigned for him,” Mr. Weiner said. “I wish this subject would have been raised with Senator Lieberman before the campaign contributions arrived.”