Observing that President Bush is “going through a rough period,” Mayor Bloomberg said his decision to greet the president at John F. Kennedy International Airport yesterday was the “nice thing to do.”

But it was more than just a courtesy call. Mr. Bloomberg also had a specific point to bring up with the president amid the smiles and handshakes: recent cuts to the city’s share of federal homeland security funding.

Mr. Bloomberg met Mr. Bush as he stepped off Air Force One yesterday morning, and the two engaged in what the mayor described as “a pleasant chit chat” before the president boarded a helicopter to give a commencement address at the United States Merchant Marine Academy in Kings Point.

Mr. Bloomberg does not usually meet the president when he flies into the region, and lately he’s had vocal policy differences with the Bush administration.

While Mr. Bloomberg has joined a litany of local elected officials in criticizing a 40% cut to the city’s share of federal grants, he actually thanked the president yesterday for his support on the issue and indicated that Congress deserves most of the blame.

“What I said to him was I appreciated his focus on distributing money, his public position on distributing Homeland Security money based on threat and threat alone, and that I was disappointed that Congress hasn’t done that,” Mr. Bloomberg told reporters at a ribbon-cutting near Times Square later in the day.

Mr. Bloomberg had harsher words for lawmakers in the House and Senate. “The real problem is that with Congress, decisions don’t get made based on rational thought and analysis,” he said. “They get made on partisan politics, where everybody feels obliged to bring home part of every pot of money for their constituents.”

The mayor will testify tomorrow in Washington before the House Homeland Security Committee, which is chaired by Rep. Peter King, a Republican of Long Island.

Mr. Bloomberg’s remarks drew criticism from Rep. Anthony Weiner, a Democrat representing Brooklyn and Queens. “The mayor blew it,” Mr. Weiner said. “It is Bush’s Department of Homeland Security that has been slashing New York in favor of Omaha, Neb.”

Rep. Vito Fossella, a Republican representing Staten Island and part of Brooklyn, said he also spoke to Mr. Bush this morning about the cuts to federal anti-terror funding. He said he told the president that the grant allocation didn’t make sense. “He said he understood, but beyond that, there were no commitments,” Mr. Fossella said.

Mr. Fossella had earlier called on the White House to intervene on behalf of the city, and he said he still held out hope that more funding would be forthcoming. “The purpose here is to keep the fire brewing, and not to forget about this issue,” he said. In contrast to Mr. Weiner, Mr. Fossella said the White House was beginning to understand the problem, and he agreed with Mr. Bloomberg’s criticism of Congress. “Clearly I think many in the Congress needs to change their ways and change their methods,” Mr. Fossella said.

The fact that Mr. Bloomberg chose to meet Mr. Bush at all was notable, since the mayor has repeatedly criticized the administration since his second term began in January.

“You can’t go every time the president comes to the city and rush out there. I have a job to do as well,” he said. “I think the president of the United States deserves the respect of the office, whether you agree with him or not.”

The president’s recent struggles in the polls also played into the thinking of the mayor, whose approval ratings have remained high following a landslide re-election victory. “It was the nice thing to do, and I felt this time he’s going through a rough period,” Mr. Bloomberg said, before quickly adding: “There’s no question that I disagree with this administration on a lot of things, and I’ve never been reticent to say that, but I still respect the government, as all New Yorkers do.”