But Rumsfeld said on Saturday he had not asked the Muslim country to send peacekeeping troops to Iraq.
Rumsfeld, the first American defence secretary ever to visit this poor South Asian country, met Bangladeshi Prime Minister Begum Khalida Zia, Foreign Minister Murshid Khan and senior
Khan expressed willingness to send peacekeeping troops to any country that needed them as long as the troops were welcome and operated under UN control, but he gave no further details.
The United States and Britain are pressing for a new UN resolution under which the world body might authorise an international peacekeeping force in Iraq.
Speaking earlier to an Asian security conference in Singapore, Rumsfeld denied that Washington was pressing its Asian allies to support the US-led occupation in Iraq.
Washington has been particularly keen, but as yet unsuccessful, to recruit Muslim nations for occupation tasks in Iraq.
In Dhaka, hundreds gathered on the streets on Saturday shouting "Go back Rumsfeld," and "Rumsfeld, your hands are red with blood of Iraqis." They burned an American flag.
The protesters were from the Islamic Constitution Movement, one of about two dozens Islamist and leftist parties that staged similar anti-US protests on Friday. They also burned American flags and chanted "Killer Rumsfeld go back".
Demonstrators in Dhaka chant
'Killer Rumsfeld go home'
More than 6000 police and paramilitary troops fanned out across the city on Saturday after an overnight arson attack on a double-decker bus killed nine people and injured at least 20.
Dhaka's metropolitan police commissioner, Ashraf al-Huda, told reporters after the attack that "setting fire to vehicles has become a tradition ahead of opposition strikes".
Dhaka considers the visit as a seal of US trust in Bangladesh's firm stance against "terrorism" and recognition for the Muslim-majority country as a moderate democracy, officials said.