By Chris Buckley and Doug Palmer
WASHINGTON (Reuters) - China's Vice President Xi Jinping on Wednesday offered deeper cooperation with the United States on trade and hot spots like North Korea and Iran, but warned Washington to heed Beijing's demands on Tibet, Taiwan and other contentious issues.
"Sino-U.S. relations stand at a new historic starting point," China's expected next leader told U.S. business groups after meetings on Tuesday with President Barack Obama and other top U.S. officials.
China and the United States should strive to create "a new type of great power relationship for the 21st century," Xi said.
But he said the two powers also had to "strive to avoid misunderstandings and avert misjudgments" and should "truly respect each other's core interests and major concerns."
Xi's visit to United States this week presents a chance for him to boost his international standing before his expected promotion to head of China's communist party later this year and president of the world's most populous nation in 2013.
Even as Xi continued his U.S. visit, Obama, at a campaign-style stop in Milwaukee, took aim at China's trade practices, saying he will not stand idly by when American's competitors "don't play by the rules."
"I directed my administration to create a Trade Enforcement Unit with one job: investigating unfair trade practices in countries like China," Obama told factory workers.
Xi met with House of Representatives Speaker John Boehner and Senate Majority Harry Reid on Wednesday morning and after his speech was headed to Iowa for the next leg of his trip, which finishes later this week in Los Angeles.
Xi addressed a number of sore spots in the U.S.-China relationship, including Beijing's currency policy.
Many U.S. lawmakers complain the yuan is significantly undervalued, giving Chinese companies an unfair price advantage that helped lift the U.S. trade deficit with China to a record $295.5 billion in 2011.
Xi said currency reforms already taken by Beijing helped boost U.S. exports to China to more than $100 billion in 2011 and has significantly reduced China's overall trade surplus.
"China has become the United States' fastest growing export market," Xi said. "The trade surplus as a proportion of GDP has been falling from over seven percent to two percent, at a level internationally recognized as reasonable."
U.S. Treasury Secretary Geithner acknowledged on Wednesday that Beijing is gradually letting its currency rise, but not fast enough to please the United States.
"We think they have some ways to go, we would like them to move more quickly," he told a congressional panel.
Xi is poised to become China's next leader following a decade in which it has risen to become the world's second largest economy while the United States has fought two wars and endured the deepest and longest recession since the Great Depression that sapped its resources.
"The world is currently undergoing profound changes, and China and the United States face shared challenges and shared responsibilities in international affairs," Xi said.
"We should further use bilateral and multilateral mechanisms to enhance coordination between China and the United States on hotspots, including developments on the Korean peninsula and the Iran nuclear issue," he said.
At the same time, he urged Washington not to support movements in Taiwan and Tibet for independence.
China deems the self-ruled island of Taiwan to be an illegitimate breakaway from mainland rule since 1949, and has warned that the island must accept eventual reunification.
In recent years, tensions between the two sides of the Taiwan Strait have eased as economic flows have grown. But Beijing remains wary of U.S. involvement in the issue, which it calls an internal affair.
In early 2010, the Obama administrations decision to move forward with proposed arms sales to Taiwan triggered vehement criticism from Beijing, including warnings of sanctions against U.S. companies involved in the sales. Those warnings petered out, but Xi made clear that Taiwan remains an acute concern for Beijing's dealings with Washington.
Tensions over Chinese control of Tibet have flared in past months when a succession of protests and self-immolations have exposed volatile discontent. Chinese officials have repeatedly blamed those tensions on separatists or supporters of the Dalai Lama, the exiled Buddhist leader of the region.
Xi also acknowledged the Obama administration's recent "pivot" toward Asia, but warned it not to push too far.
"China welcomes the United States playing a constructive role in promoting the peace, stability and prosperity of the Asia-Pacific region, and at the same time we hope the U.S. side will truly respect the interests and concerns of countries in the region, including China."
(Additional reporting by Rachelle Younglai in Washington and Laura MacInnis in Milwaukee; editing by Anthony Boadle)