(CBS) The FBI has received unconfirmed information from intelligence sources overseas that hospitals in four U.S. cities could be the targets of a terrorist threat.

This latest threat comes as counter-terrorism officials say the chances of al Qaeda terrorism against the U.S. remains high even though specific information remains scarce.

Houston FBI spokesman Bob Doguim said Wednesday night the vague threat involved hospitals in Houston, San Francisco, Chicago and Washington, D.C., and mentioned a time between December and April.

"It's non-specific, uncorroborated information, but nonetheless it is information we received," Doguim said.

He said the threat mentions the possibility of anthrax or explosives.

"The alleged attack would take place in reaction to the continued arrest of a Pakistani nationals by Pakistani authorities," according to an FBI statement.

A statement from the Chicago FBI office said the threat suggested an attack was timed for mid-December and the holidays.

"We've always been on a state of high alert," Chicago officer Carlos Herrera said. "That hasn't changed."

There's been a drumbeat of warnings from officials who should know.

Attorney General John Ashcroft: "I think al Qaeda remains an active threat to the United States."

CIA Director George Tenet: "They have reconstituted. They're coming after us. They want to execute attacks."

FBI Director Robert Mueller: "There may be individuals in the United States who we do not know about who could commit attacks."

And Richard Shelby, ranking member of the Senate Intelligence Committee: "We don't know when, we don't know where, but the likelihood is great."

Some worry attacks could come now during the Muslim holy month of Ramadan or in response to the scheduled execution of Aimal Kasi, the Pakistani man who killed two CIA employees nearly ten years ago.

Terrorism expert Brian Jenkins says, in fact, an attack could come at any time.

"The terrorists are very opportunistic, they will attack when and where they can and with any means they can mobilize," he told CBS News Correspondent Bob Orr.

A senior law enforcement official, speaking Tuesday on condition of anonymity, said the amount of intelligence about potential attacks on the United States and its allies has increased this month, rising again to the level before the Sept. 11 attacks.

Gordon Johndroe, the Homeland Security spokesman, said Tuesday that recent warnings about attacks against railways, oil and gas and other economic targets remain in effect.

"There is intelligence, while it is general, that has pointed to and raised concerns about our critical infrastructure," he said.

It is not specific enough to raise the nationwide alert level, which remains at code yellow — the middle of five threat levels -- because of a lack of specific details on where and when an attack may occur, Johndroe said. Yellow means "significant risk of terrorist attacks."

Last month's public warnings -- issued Oct. 9 and Oct. 23 -- came in part from the release of taped statements from high-level al Qaeda leaders threatening new attacks. Counter-terrorism officials regard them as calls to action for field operatives.

The latest tape, with a voice claiming to be Osama bin Laden, was aired Tuesday on al-Jazeera. If validated, the tape would be regarded as significant because it made reference to recent events, the first hard evidence in a year that bin Laden was alive.

In addition, U.S. law enforcement officials said the talk that intelligence is picking up surrounding next week's NATO summit in Prague is similar to what they heard before the July 2001 G-8 summit in Genoa, Italy.

As they did in Genoa, where the gathering of world leaders passed without terrorist incident, security officials are considering closing the Prague city center to all but summit personnel.

Some recent warnings in Europe stem from the same intelligence that led to the U.S. warnings, Bush administration officials said.

Security was increased at a number of European ferry ports and at NATO headquarters in Brussels, Belgium. Counter-terrorism authorities also remained concerned about al Qaeda strikes in the Middle East.