(Adds Rice interview with FOX News, paragraphs 4-5)

By David Morgan

WASHINGTON, July 12 (Reuters) - U.S. Homeland Security Secretary Michael Chertoff said on Thursday the threat to the United States from al Qaeda has not returned to levels seen just before the Sept. 11 attacks nearly six years ago.

Chertoff played down media reports that the militant network was now as great a threat to U.S. soil as in the months before the Sept. 11 attacks on Washington and New York.

"I wouldn't put it at that level," he told ABC's "Good Morning America." "I do think we've accomplished an awful lot in dismantling their activities overseas and in building our own defenses. But I do think the level of intent on the part of the enemy remains very high."

U.S. Secretary of State Condoleezza Rice said in an interview with FOX News that she was also concerned about the threat from al Qaeda but made clear there was nothing that appeared "concrete or imminent" in terms of planned attacks.

"It's a period of time in which there is a lot of intelligence, a lot of chattering that would suggest that there's an effort to plan an attack against the United States," said Rice.

The Washington Post reported the militant network has significantly rebuilt itself and established a safe haven in remote tribal areas of western Pakistan. It cited a new intelligence report to be reviewed by Chertoff and other top officials at a White House meeting later Thursday.

Top intelligence analysts also told Congress on Wednesday that al Qaeda's training activities, funding and communications have increased as the militant network has settled into new bases in remote areas of Pakistan.

Chertoff told the Chicago Tribune this week that his "gut feeling" was that the United States faced a heightened risk of attack this summer.

But he told NBC on Thursday: "We don't have any specific information about an imminent or near-term attack on the homeland. We're looking at the strategic picture over the next six months to a year. We're evaluating where that is."

He said his concern the United States could be entering a period of heightened risk was based on greater al Qaeda activity in Pakistan and Africa, an increase in public messages from militant figures including Osama bin Laden's second-in-command, Ayman al-Zawahri, and a history of summer attacks.

(Additional reporting by Sue Pleming)

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