WASHINGTON – With a Republican congressman from Long Island set to hold private negotiations today with a senator from Maine about increasing New York’s share of the federal anti-terrorism pie, two Maine congressmen who voted last spring against increasing the share for states such as New York reaffirmed their commitment to the current spending formula.

The House of Representatives agreed by an overwhelming 409 to 10 vote in May to lower to 0.25% from 0.75% the minimum share of federal homeland security dollars that each state receives. Of the 10 congressmen who voted against the change, which would effectively increase the money that goes to high-risk locales like Washington, D.C., and New York City, two were from Maine.

The chairman of the independent 9/11 Commission that was established, in part, to offer recommendations for avoiding another terrorist attack on American soil, Thomas Kean, said last week that while he thinks security funds should be allocated strictly according to risk, the House bill is acceptable to him as a compromise.

Earlier this month, Mr. Kean said that allocation formulas based on anything other than risk are “scandalous.”

Mr. Kean’s comments were seen at the time as giving leverage to those who have pressed the Senate to adopt a bill similar to the one in the House. But the Republican chairman of the Senate Committee on Homeland Security, Senator Collins, of Maine, has defended a bill she proposed that would send no less than 0.55% of federal antiterrorism funds to each state, regardless of risk.

Mr. King, who took over as chairman of the House Committee on Homeland Security in September, said he hopes a compromise with Ms. Collins can be reached.

“I have no reason to think there is any magic solution in sight, but the fact that she wants to meet, and I want to meet, and our staffs have established a relationship – we’re trying to get this to work – is a good sign,” Mr. King told The New York Sun late last week. “I don’t know how dug-in she is, so I don’t know how much room there is for compromise.”

A spokesman for Rep. Thomas Allen, one of the two Maine congressmen who voted against the House bill, said that Mr. Allen stands by his earlier vote on the ground that high-risk areas are not always efficient with their money and that Maine deserves what it gets because of its long international border and coastline.

“Tom has supported the 9/11 commission and its finding and recommendations,” Mr. Sullivan said. “It’s not that more money shouldn’t be sent to urban areas, it’s that the pie of homeland security funding isn’t large enough to meet all the nation’s needs.”

Rep. Michael Michaud, another Democrat from Maine who voted against the House version of the bill, also stood by his earlier vote. Asked if Mr. Michaud thinks a risk-based formula for allocating anti-terrorism dollars is still a bad idea, even after Mr. Kean’s comments, his spokeswoman, Monica Castellanos, referred a reporter to his statement from May.

“I think it is still very appropriate,” Ms. Castellanos wrote in an e-mail.