ULAANBAATAR, Mongolia (CNN) -- U.S. President George W. Bush thanked Mongolia Monday for standing with the United States in Iraq in an historic visit to the struggling Asian democracy sandwiched between China and Russia."Both our nations know that our responsibilities in freedom's cause do not end at our borders -- and that survival of liberty in our own lands increasingly depends on the success of liberty in other lands," Bush said in a speech to the Mongolian parliament.After decades of being ruled by a communist regime, Mongolia has been governed by a democratic coalition party since parliamentary elections in 2004.Bush's visit to Mongolia was the first by a sitting U.S. president to the country, a sparsely populated Buddhist nation of 2.7 million people.Mongolia has 131 troops in Iraq and about 50 to Afghanistan in support of the U.S. war against terrorism, clinching its status as an ally."The Mongolian Armed Forces are serving the cause of freedom -- and the United States armed forces are proud to serve beside such fearless warriors," Bush said on the last stop of his tour, following two days of talks with Chinese leader Hu Jintao. The descendants of Genghis Khan, whose empire once spanned from Southeast Asia to Hungary, fear being overshadowed by China's massive economy, and are keenly eyeing the prospect of more American money through a new U.S. aid program known as the Millennium Challenge Account. (Full story)Bush said on Monday that Mongolia's help in the war on terror was being rewarded with $11 million, which he said were "critical funds to help you improve your military forces, so we can continue working together for the cause of peace and freedom." China's influence over the economy has become overwhelming, eclipsing Russia in most areas except oil, which Mongolia imports from Siberia.Iraq dogs BushWhile the United States has an ally in Mongolia, the debate over America's commitment in Iraq has dogged Bush during his eight-day tour of Asia, with growing doubts back home distracting him from promoting U.S. economic and political interests in Asia.The president spent part of his visit to Beijing responding to heated political rhetoric back home.He called an influential Democrat who wants U.S. troops home from Iraq a good man, but wrong. (Full story)"I know the decision to call for an immediate withdrawal of our troops by Congressman Murtha was done in a careful and thoughtful way. I disagree with his position," he said.This was a noticeably toned down response compared to a White House statement just days earlier, linking hawkish Congressman John Murtha to liberal filmmaker Michael Moore.Murtha on Thursday said the United States should pull out from Iraq over a six-month period. The retired Marine colonel said he had concluded that the presence of U.S. troops was counterproductive because they had become a magnet for insurgent violence.During his second stop in South Korea, Bush was dogged by anti-war protests, and a surprise proposal from his host to pull a third of its troops out of Iraq. But Bush has remained resolute, saying that leaving Iraq prematurely is "not going to happen, so long as I'm the president."Pressure on ChinaThe president spent Sunday morning church in Beijing, one of five sanctioned and censored by the communist government.Later Bush took the call to broaden rights for China's 1.3 billion people to its leader Hu.Bush said the United States has given Beijing a list of dissidents it believes are "improperly imprisoned," and he seemed encouraged that the Chinese leader even mentioned human rights. "Those who watch China closely would say that maybe a decade ago a leader wouldn't have uttered those comments," Bush said. "He talked about democracy." But with reports of a pre-Bush visit crackdown on dissidents, Secretary of State Condoleezza Rice had earlier expressed dismay, not progress."We've certainly not seen the progress that we would expect and we'll have to keep working on it," Rice said.The president spent much of his talks pouring over economic differences with the Chinese powerhouse that puts the U.S. at a huge disadvantage.On Sunday Bush pressed his Chinese counterpart to expand the country's religious, political and social freedoms. The U.S. trade deficit with China was also high on the agenda. (Full story)Hu promised to take action on the issue, but provided no concrete plan.Bush did win concessions for action on China's undervalued currency, or expected $200 billion trade deficit, and Bush aides reported some promises from China's premier about another major issue: piracy.Counterfeit products sold freely at markets in China and exported around the world cost Americans an estimated 750,000 jobs a year, and American business $250 billion. Experts say China makes the bulk of pirated copyright material.Later, the president took an hour-long bike ride with Chinese Olympic hopefuls, jokingly asking them how to say "let's keep up with this old man" in Chinese. CNN's Dana Bash contributed to this reportCopyright 2005 CNN. All rights reserved.This material may not be published, broadcast, rewritten, or redistributed. Associated Press contributed to this report.