For now, US special forces are on a scouting mission
The commandos are carrying out scouting and reconnaissance missions, but are not actively hunting for the prime suspect Osama bin Laden, the unnamed official said.
The BBC defence correspondent says the news sends a signal to the American people that military groundwork is in hand to respond to the 11 September attacks on the United States.
To the Taleban, he says, the message is that the US means business, and the time has come to hand over Bin Laden.
On Friday, US Attorney General John Ashcroft released a letter which linked the hijackers of the three planes that crashed into the World Trade Center and the Pentagon.
Mr Ashcroft said the letter was found in a piece of luggage belonging to Mohamed Atta, 33, an Egyptian suspected of being one of the leaders of the hijackers.
"This letter is clear evidence linking the hijackers on three separate flights," Mr Ashcroft said.
In other developments:
'Shocking view'
The four-page letter was, according to one BBC correspondent in Washington, part-instruction manual for the hijackers and part-prayer book.
Mr Ashcroft said it gave a "disturbing and shocking view
into the mind-set of these terrorists".
In addition to the copy found in Mohamed Atta's luggage, Mr Ashcroft said two more were found.
One was in a vehicle parked by another hijacker at Dulles airport, near Washington, and a third in the wreckage of the hijacked plane which crashed in Pennsylvania.
"Mention much the name of God," the letter said, adding that the group were about to meet "the creator of the heavens and earth."
Mid-East co-operation
On Friday, President Bush said he was most pleased with the co-operation the US was getting from countries in the Middle East for its global campaign against terrorism.
He held talks with Jordan's King Abdullah, who offered the United States his full and unequivocal support, saying those who had carried out the attacks had acted "completely against all the principles that Arab and Muslims believe in".
After the talks President Bush gave the king a pen he had used earlier in the day to sign a free trade pact with Jordan.
He said Islam was a religion of love, peace and compassion - the opposite of the al-Qaeda network linked to Osama Bin Laden, which Mr Bush said was based on evil.
King Abdullah has linked his condemnations of the attacks with a message that any war against terrorism should be linked to renewed efforts to resolve the Israeli-Palestinian conflict.
Mr Bush also said he was particularly impressed by help from Saudi Arabia.
BBC correspondents say this apparently confirms reports that Saudi Arabia has decided to allow US forces to make use of a vital command centre launch at a military base outside Riyadh.
Mr Bush ruled out further negotiation with the Taleban leaders of Afghanistan, where Bin Laden is being sheltered.