Mr Rumsfeld arrived in the Saudi capital Riyadh on Wednesday in an attempt to drum up support for the US-led coalition against terror.
The American defence secretary is also due to visit Oman, Egypt and Uzbekistan - which borders on Afghanistan.
Meanwhile France has agreed to allow the United States to use its airspace and says it will also co-operate with the US Navy in the Indian Ocean.
And the United States has given its Nato allies a list of requests for specific assistance in the fight against terrorism.
Nato spokesman Yves Brodeur declined to disclose details, but said the list included both military support and more indirect help.
Mr Brodeur said there was no deadline for a response and no demands had been made of individual countries.
The request was made in the framework of Article 5 of the Nato treaty - a mutual defence clause which became fully operational on Tuesday when the alliance accepted Washington's evidence that Bin Laden was linked to the 11 September attacks on the US.
Intelligence the 'key'
Mr Rumsfeld said intelligence, not military action, would be the key to breaking Osama Bin Laden's Al-Qaeda network.
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"It's not going to be a cruise missile or a bomb that's going to be the determining factor," Mr Rumsfeld said in an interview en route to the Saudi capital, Riyadh.
"It's going to be a scrap of information from some person in some country that's been repressed by a dictatorial regime... that's going to enable us to pull this network up by its roots and end it."
Military presence
The United States has maintained a major military presence in the Gulf since the end of the Gulf War in 1991.
In addition, it has massed about 30,000 military personnel in two aircraft carriers - the USS Carl Vinson and the USS Enterprise - and 350 planes in the Gulf and Arabian Sea.
Two more carriers are also heading for the region - the USS Theodore Roosevelt and USS Kitty Hawk.
And there were reports that another 1,000 troops were on their way to the region from New York State.
The Washington Post said the troops were bound for Uzbekistan and Tajikistan and would be used mainly as security for air and rescue forces already there.
It's not going to be a cruise missile or a bomb ... it's going to be a scrap of information... that's going to enable us to pull this network up by its roots
US Defence Secretary Donald Rumsfeld
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Military build-up alarms Gulf Arabs
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Uzbekistan backs 'unnatural' ally
(02 Oct 01 | Asia-Pacific)
Blair promises victory over terror
(02 Oct 01 | UK Politics)
Bin Laden's 'cash link' to hijackers
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When will military action begin?
(26 Sep 01 | Americas)
Q&A: Covert operations
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