The leader of the embattled Taliban, Mullah Mohammad Omar, made the threat in a telephone interview with the BBC earlier this week.
Omar dismissed Taliban military reverses, and insisted that "the current situation in Afghanistan is related to a bigger cause, that is the destruction of America."
Asked whether he had a "concrete plan" to implement the destruction of the United States, Omar responded, "The plan is going ahead and, God willing, it is being implemented. But it is a huge task, which is beyond the will and comprehension of human beings.
"If God's help is with us, this will happen within a short period of time," Omar added, according to the BBC. "Keep in mind this prediction."
However, when asked whether his threat and "plan" were related to claims by Osama bin Ladin to have nuclear and biological weapons, Omar sounded less like a terrorist than a zealot hoping for a miracle.
"This is not a matter of weapons," the BBC quoted Omar as saying. "We are hopeful for God's help. The real matter is the extinction of America. And, God willing, it will fall to the ground."
In Washington, the senior U.S. official, who is familiar with national security concerns, was both dismissive and cautious.
"We do not give his threat too much credibility," the official said. "However, at this time we are taking all threats" -- regardless of credibility -- "very, very seriously."
Meanwhile, the Justice Department is continuing to seek interviews with more than 5,000 immigrant men between the ages 18 and 33 who have entered the United States since Jan. 1, 2000, from countries considered likely venues for terrorist plotting.
The department has said the men are not terrorist suspects, but may have information relating to others who are.
The interviews are being carried out, in large part, by state and local law enforcement at the request of the 94 U.S. attorneys offices across the country.
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