John Brennan, Obama's counterterrorism adviser, declined to provide details on the incident or say whether the activist, Chen Guangcheng, might be hiding in the U.S. embassy in Beijing as reported.
Chen, who has exposed forced abortions and sterilizations in villages as a result of China's one-child policy, escaped house arrest a week ago in Shandong province in eastern China. Chinese-based activists say he was driven away by supporters and then handed over to others who brought him to Beijing.
"I think in all instances the president tries to balance our commitment to human rights, making sure that the people throughout the world have the ability to express themselves freely and openly, but also that we can continue to carry out our relationships with key countries overseas," Brennan told "Fox News Sunday."
The U.S. relationship with China is "very important," he added, "so we're going to make sure that we do this in the appropriate way and the appropriate balance is struck."
Chen's escape comes at a politically sensitive time for the U.S. This week, Secretary of State Hillary Rodham Clinton and Treasury Secretary Timothy Geithner head to Beijing for long-planned strategic and economic talks. Assistant Secretary of State Kurt Campbell began a hurried mission to Beijing on Sunday to smooth the way for annual talks involving Clinton and Geithner.
The U.S. has been looking to China for help on trying to curb suspected nuclear ambitions of North Korea and Iran, and to push Syria toward a cease-fire with anti-government protestors. Bilateral disputes over trade, China's currency and U.S. relations with Taiwan also were expected to surface during the talks.
While the White House has remained mostly mum on the incident -- and how much it might factor into next week's discussions -- Brennan suggested that the diplomatic dance with China isn't new.
"I think it would be fair to say the president has faced similar situations in the past in terms of this balancing requirement and so I'm confident that the president and others within the U.S. government will be able to find the right way forward," Brennan said.
Presumptive Republican presidential nominee Mitt Romney expressed his concern Sunday for the safety of Chen and his family, urging U.S. government officials to offer the dissident and his family protection.
"My hope is that U.S. officials will take every measure to ensure that Chen and his family members are protected from further persecution," Romney said early Sunday in a statement. "Our country must play a strong role in urging reform in China and supporting those fighting for the freedoms we enjoy."
While Chen escaped a week ago from Dongshigu village and made it 370 miles northwest to Beijing, his wife and 6-year-old daughter were left behind. The whereabouts of several other relatives, including Chen's mother and brother, are unknown.
Seven lawyers have volunteered to defend Chen's nephew, Chen Kegui, who allegedly confronted and stabbed local officials who stormed his house in the middle of the night on Thursday in apparent retribution for the activist's escape.