"They continue to adapt and rebuild," Michael Chertoff told CBS's The Early Show. "The message, again, for us is we have to continue to be vigilant."
Chertoff, however, added that security officials "don't have any specific information about an attack against the homeland in the near future."
Chertoff's comments follow the latest threat assessment from U.S. counterterrorism analysts who say al Qaeda has used its safe haven along the Afghan-Pakistan border to restore its operating capabilities to a level unseen since the months before Sept. 11, 2001.
A counterterrorism official familiar with a five-page summary of the document — titled "Al Qaeda better positioned to strike the West" — called it a stark appraisal. The analysis will be part of a broader meeting at the White House on Thursday about an upcoming National Intelligence Estimate.
The official and others spoke to The Associated Press on condition they not be identified because the report remains classified.
The findings suggest the network that launched the most devastating terror attack on U.S. soil has been able to regroup despite nearly six years of bombings, war and other tactics aimed at dismantling it.
Meanwhile, An American Airlines flight from Los Angeles to London was
after the flight crew reported what they thought was a suspicious person on board. Officials have interviewed the person and sources told CBS News there is no connection to any terror plot.
The threat assessment the White House will review focuses on the terror group's safe haven in Pakistan and makes a range of observations about the threat posed to the United States and its allies, officials said.
Counterterrorism officials have been increasingly concerned about al Qaeda's recent operations. This week, Chertoff said he had athat the United States faced a heightened risk of attack this summer.
Asked to clarify the phrase, Chertoff told The Early Show his comments were based on "an informed opinion."
Still, numerous government officials say they know of no specific, credible threat of a new attack on U.S. soil.
The counterterrorism official, paraphrasing the report's conclusions, said Al Qaeda is "considerably operationally stronger than a year ago" and has "regrouped to an extent not seen since 2001. They are showing greater and greater ability to plan attacks in Europe and the United States."
The group also has created "the most robust training program since 2001, with an interest in using European operatives," the official quoted the report as saying.
At the same time, this official said, the report speaks of "significant gaps in intelligence" so U.S. authorities may be ignorant of potential or planned attacks.
John Kringen, who heads the CIA's analysis directorate, echoed the concerns about al Qaeda's resurgence during testimony and conversations with reporters at a House Armed Services Committee hearing on Wednesday.
"They seem to be fairly well settled into the safe haven and the ungoverned spaces of Pakistan," Kringen testified. "We see more training. We see more money. We see more communications. We see that activity rising."
The threat assessment comes as the 16 U.S. intelligence agencies prepare a National Intelligence Estimate focusing on threats to the United States. A senior intelligence official, who spoke on condition of anonymity while the high-level analysis was being completed, said the document has been in the works for roughly two years.
Kringen and aides to National Intelligence Director Mike McConnell would not comment on the details of that analysis.
"Preparation of the estimate is not a response to any specific threat," McConnell's spokesman Ross Feinstein said, adding that it probably will be ready for distribution this summer.
Kringen said he wouldn't attach a summer time frame to the concern. In studying the threat, he said he begins with the premise that al Qaeda would consider attacking the U.S. a "home run hit" and that the easiest way to get into the United States would be through Europe.
Several European countries — among them Britain, Denmark, Germany and the Netherlands — are highlighted in the threat assessment partly because they have arrangements with the Pakistani government that allow their citizens easier access to Pakistan than others, according to the counterterrorism official.
This is more troubling because all four are part of the U.S. visa waiver program, and their citizens can enter the United States without additional security scrutiny, the official said.
The Bush administration has repeatedly cited al Qaeda as a key justification for continuing the fight in Iraq.
"The No. 1 enemy in Iraq is al Qaeda," White House press secretary Tony Snow said Wednesday. "Al Qaeda continues to be the chief organizer of mayhem within Iraq."
The findings could bolster the president's hand at a moment when support on Capitol Hill for the war is eroding and the administration is struggling to defend its decision for a military buildup in Iraq.
The threat assessment says that al Qaeda stepped up efforts to "improve its core operational capability" in late 2004 but did not succeed until December of 2006 after the Pakistani government signed a peace agreement with tribal leaders that effectively removed government military presence from the northwest frontier with Afghanistan.
The agreement allows Taliban and al Qaeda operatives to move across the border with impunity and establish and run training centers, the report says, according to the official.
It also says that al Qaeda is particularly interested in building up the numbers in its middle ranks, or operational positions, so there is not as great a lag in attacks when such people are killed.
"Being No. 3 in al Qaeda is a bad job. We regularly get to the No. 3 person," Tom Fingar, the top U.S. intelligence analyst, told the House panel.
The report also notes that al Qaeda has increased its public statements, although analysts stressed that those video and audio messages aren't reliable indicators of the actions the group may take.