Bin Laden and Afghanistan are the targets - for now
Asked about the next stage of military action, Mr Powell made it clear the focus would remain on Osama Bin Laden's al-Qaeda network and, by implication, Afghanistan.
"We will be patient, we will be determined, to not only get rid of the al-Qaeda network, but to deal with terrorism around the world," he said.
Mr Powell's comments came after the US told the United Nations that it reserved the right to pursue military action against other countries found to be harbouring terrorism suspects.
Possible targets
There has been speculation that Iraq could be targeted by the US, fuelling Arab fears that the campaign could widen to take in long-standing US enemies.
Reports in the New York Times newspaper also suggested that groups in the Philippines, Indonesia and Malaysia, which have been linked to al-Qaeda, could also be attacked.
But the BBC State Department correspondent, Jon Leyne, says Mr Powell's comments are yet another strong indication that Washington is very wary of using military force to further the campaign elsewhere in the world.
His comments were supported by the UK Government, which set out its aims in the attacks on Afghanistan.
Objectives
An official travelling with UK Prime Minister Tony Blair, who is trying to rally Arab support for the US-led campaign against terror, said there were four initial objectives:
Earlier on Wednesday, Mr Powell dismissed a defiant statement by al-Qaeda which threatened more attacks on the US.
"It is a chilling challenge but I assure you we will meet that challenge," Mr Powell said on American television.
The secretary of state said that despite anti-American protests in some countries, Arab nations have been very supportive of the US-led attacks on Afghanistan.
Foreign ministers from across the Muslim world have strongly condemned last month's attacks on the United States, but have also warned against targeting any Arab or Islamic country other than Afghanistan under what they called the pretext of combating terrorism.
The statement from the Organisation of the Islamic Conference - which represents more than one-billion Muslims worldwide - came on Wednesday at the end of an emergency meeting in Qatar.