Gov. George Pataki, criticized for failing to demand more anti-terrorism help from the Bush administration, called on the federal government to give New York a bigger share of homeland security funds.

Meanwhile, Black Hawk helicopters and infrared-equipped planes have begun flying over New York City under tightened security measures implemented around the start of war in Iraq, officials said Tuesday.

Pataki on Tuesday called for a "threat-based allocation system" in which more prominent targets such as New York City receive more security funding. The current system has given some states almost seven times more per capita than New York, Pataki noted in a letter to Homeland Security Secretary Tom Ridge.

"I believe the allocation formula doesn't properly recognize New York and other places that are symbols of American freedom," Pataki told reporters after a visit to an Air National Guard facility near Schenectady. "The formula doesn't reflect the extraordinary costs that we have incurred."

Ridge spokesman Brian Roehrkasse said the secretary shared the governor's concerns and would work with Congress to address them. Although no specific plan had been formulated, he said, "New York will receive significant funding."

Pataki previously had avoided publicly discussing the need for Washington to contribute more to his state's homeland security. New York Democrats have fueled speculation that Pataki may want a Cabinet position or have hopes of becoming President Bush's running mate next year if Vice President Dick Cheney decides not to seek re-election.

Pataki on Tuesday called such suggestions "utter nonsense."

"My focus is on New York and protecting the people of New York," he said.

In his letter to Ridge, Pataki said New York state is spending an extra $7.5 million a week and New York City an extra $5 million a week on heightened security. The governor told reporters the federal government should cover all those extra costs.

Bush on Monday outlined a $75 billion appropriations bill to pay for the war with Iraq. It included $4.24 billion for homeland security, to be allocated under a formula based on population and other factors.

In New York City, the helicopters and Cessna Citation II jets, from the Department of Homeland Security's Bureau of Immigration and Customs Enforcement, began round-the-clock patrols Monday, the bureau said.

The unarmed aircraft are linked with a base in California that uses ground-based radar and computer databases to analyze threats, officials said.

Slower-moving than fighter jets, the Cessnas and Black Hawks are well suited to locating and warding off aircraft that accidentally wander into restricted airspace, bureau officials said.

In the event of an intentional threat, pilots can call in Air National Guard and active-duty aircraft patrolling over New York City.

Fighter jets under the North American Aerospace Defense Command halted their 24-hour-day, seven-day-a-week patrols over the city early last year but renewed them over the weekend, according to a federal official familiar with the plans who spoke on condition of anonymity.

City officials said the renewed patrols are a reaction to generalized warnings from law enforcement and intelligence agencies - not specific threats against New York.

"Is there a real risk? I don't think so, but that doesn't mean you don't take precautions," Mayor Michael Bloomberg said Tuesday.