GWEN IFILL: Next tonight, China's likely next leader meets the American president in Washington.
PRESIDENT BARACK OBAMA: Well, I want to welcome Vice President Xi.
GWEN IFILL: President Obama shuck struck a hopeful note as he hosted Chinese Vice President Xi Jinping at the White House today.
BARACK OBAMA: We welcome China's peaceful rise, that we believe that a strong and prosperous China is one that can help to bring stability at prosperity to the region and to the world.
GWEN IFILL: Xi arrived in Washington as the likely next president of the world's most populous nation and its second largest economy.
Mr. Obama said such power needs to be used wisely.
BARACK OBAMA: We have tried to emphasize that because of China's extraordinarily -- extraordinary development over the last two decades, that with expanding power and prosperity also comes increased responsibilities.
GWEN IFILL: Xi, speaking through a translator, also accentuated the positive in talking about the relations between the two countries.
XI JINPING, Chinese vice president (through translator): And I hope to engage with a broad cross-section of American society during my current visit, so as to deepen mutual understanding, expand consensus, strengthen cooperation, and deepen the friendship between the Chinese and American people.
GWEN IFILL: But Xi's visit comes at a time of new tensions in the U.S.-China relationship, the latest conflict, China's veto 10 days ago of a U.N. security resolution condemning the violence in Syria.
The Chinese have also objected to President Obama's pledge to shift America's military focus to the Pacific. Xi addressed that point in a carefully worded statement in Sunday's Washington Post. "We welcome a constructive role by the United States in promoting peace, stability and prosperity in the region," he wrote. "We also hope that the United States will fully respect and accommodate the major interests and legitimate concerns of Asia-Pacific countries."
China's rising economic power has become part of the U.S. presidential campaign as well, as Republicans have criticized the U.S. debt imbalance and debated building projects like the Keystone oil pipeline to support allies like Canada.
MITT ROMNEY (R): I'll approach every spending decision, every budget item with these questions: Can we afford it? And, if not, is it really worth borrowing money from China to pay for it?
NEWT GINGRICH (R): The idea of an American president making it easier for Canada to partner with China than with the United States is amazingly destructive.
GWEN IFILL: U.S. administrations have long complained of China's undervaluing its currency and of the U.S. trade imbalance with Beijing, which in 2011 widened to nearly $300 billion.
Other areas of disagreement range from Chinese theft of American intellectual property to the continued loss of American manufacturing jobs to Chinese workers.
And protesters outside the White House today complained of China's human rights record, demanding China give Tibet its freedom.
Vice President Xi responded to U.S. human rights concerns at a State Department luncheon.
XI JINPING (through translator): We are ready to conduct candid and constructive dialogue and exchanges on human rights with the United States and other countries on the basis of equality and mutual respect, with the view to enhancing understanding, narrowing differences, learning from each other and achieving common progress.
GWEN IFILL: Xi was also meeting today with business leaders, and tomorrow returns to Muscatine, Iowa, where he visited on a 1985 agricultural tour.