Police still do not know Pearl's whereabouts
"The demands that the kidnappers have placed are not demands that we can meet or deal with," Mr Powell said.
He said that detainees at Guantanamo Bay, whose conditions the kidnappers say they want to improve, were being treated humanely as confirmed by visits from various country representatives and humanitarian organisations.
His remarks followed a decision by militants believed to be holding Mr Pearl in Pakistan to postpone his execution by one day.
Mr Pearl, a correspondent for the Wall Street Journal, went missing in the port city of Karachi on 23 January. His whereabouts remain a mystery.
The little known National Movement for the Restoration of Pakistani Sovereignty has claimed it is holding the journalist.
Mr Powell said on Thursday that he was deeply concerned about Mr Pearl's safety, and that the US was doing everything it could to find and rescue him.
He added that he was sure Pakistani President Pervez Musharraf was also doing everything he could to find Mr Pearl.
'One more day'
The militants believed to be holding Mr Pearl sent a new, unsigned e-mail to Pakistani and Western media on Thursday, which read: "We will give you one more day."
In an e-mail sent on Wednesday, the group had threatened to kill him after 24 hours if its demands were not met.
The latest e-mail reiterated that "if America will not meet our demands we will kill Daniel" and "this cycle will continue and no American journalist could enter Pakistan."
It said the kidnapping of Mr Pearl, 38, was not the end and threatened a "real war on Amrikans [Americans]".
The National Movement for the Restoration of Pakistani Sovereignty has also sent photos by e-mail, showing Mr Pearl in captivity. One of them showed a gun pointing at his head.
The group has criticised the United States for not providing lawyers and trials for Pakistanis detained on terrorism-related charges. It has also demanded better conditions for detainees held by the US at Guantanamo Bay in Cuba.
The former heavyweight boxing champion Muhammad Ali - a Muslim convert - has urged the kidnappers to treat Mr Pearl "with compassion and kindness".
Mossad
The militants have accused Mr Pearl of working for the Israeli intelligence service, Mossad, and also warned other American reporters to leave Pakistan within three days.
Pakistani police say they are making progress in their investigations into the abduction. They are questioning a suspect, Mubarak Ali Shah Gilani, who has been linked to the kidnapping.
He is reported to have denied any involvement.
Police arrested Mr Gilani - an Islamic leader with whom Mr Pearl was trying to arrange an interview when he disappeared - on Wednesday.
Mr Gilani heads a small militant group, Tanzeem ul-Fuqra.
India-Pakistan spat
Police have carried out raids in several Pakistani cities in connection with the investigation.
A Pakistani spokesman, Major General Rashid Qureshi, also alleged that there was an Indian link to the kidnapping, but declined to give details.
India has dismissed Major Qureshi's comments as "ridiculous".