George Bush has become the first US president to visit Mongolia, as he concluded a week-long Asian tour.
Mr Bush is the first US president to visit Mongolia
He met Mongolian President Nambaryn Enkhbayar and thanked him for supporting the US-led war in Iraq, and for sending more than 100 troops.
A BBC correspondent says Mr Bush's visit was meant to highlight Mongolia's shift to democracy and free markets.
In Beijing on Sunday, Mr Bush called on China to expand its social, political and religious freedoms.
Mr Bush met President Enkhbayar in the Mongolian capital Ulan Bator, and held talks inside a traditional tent, known as a ger.
Mr Bush thanked Mongolia for supporting the US' war on terrorism, and said the former communist country's transition would be an example to the world.
"Like the ideology of communism, the ideology of Islamic radicalism is destined to fail - because the will to power is no match for the universal desire to live in freedom," Mr Bush said.
Mr Bush was in Mongolia, an isolated outpost sandwiched between Russia and China, for four hours.
The country is made up mainly of pasture and desert and has an economy largely dependent on livestock and textiles. People on average earn $400 a year.
Security has been tightened ahead of Mr Bush's visit
But the US sees Mongolia as playing an important part in spreading economic and political reform in the region, says our correspondent.
Over the last seven years, the US has provided Mongolia with more than $100m in technical assistance and training for its democratic and economic reform programme.
US officials also helped draft the country's constitution in 1992 and have since helped in voter education and other pro-democracy projects.
A senior Bush administration official said Mr Bush wants to thank the country for its contribution of troops for peace-keeping missions in Iraq.
But he also wants "to give a boost to a country that's really moving in the right direction, and show that even a country that's far away or remote, if it's making the right choices, the US is going to stay with them," the official said.
In China, Mr Bush attended a service at one of the few officially-recognised Christian churches in Beijing to show his support for expressions of faith in China.
In talks with his Chinese counterpart Hu Jintao, Mr Bush also discussed trying to reduce Beijing's huge trade surplus with the US.