The gestures were warm, but tensions over the naval incident remain
The US and China will work together to avoid more confrontations in the future, Secretary of State Hillary Clinton has told reporters.
She was speaking after meeting China's Foreign Minister Yang Jiechi - but the dispute over a weekend confrontation in the South China Sea is rumbling on.
Meanwhile, Mrs Clinton warned North Korea could face "a range of options" if it goes ahead with a missile test.
Mr Yang is in Washington, and will meet US President Barack Obama on Thursday.
"We have each stated our positions, but the important point of agreement coming out of my discussions with Minister Yang is that we must work hard in the future to avoid such incidents and to avoid this particular incident having consequences that are unforeseen," Mrs Clinton told reporters after her meeting with Mr Yang.
She said his visit was a "very positive" development and that she looked forward to building a "positive, co-operative and comprehensive relationship".
Earlier, Mr Yang said he was in Washington "to get prepared for our two heads of state's meeting in London [for a G20 summit in April] and to work together to push our relations forward", according to China's official news agency Xinhua - but he made no reported mention of the maritime dispute.
SOUTH CHINA SEA TENSIONS
Territorial claims from China, the Philippines, Taiwan, Brunei, Vietnam and Malaysia overlap in resource-rich sea
Hosts some of the world's busiest shipping lanes
China says the US was in its Exclusive Economic Zone - but the two sides disagree on what activities are allowed in an EEZ
Despite the warm words, the dispute over the incident remains unresolved.
The Pentagon says five Chinese ships harassed an unarmed US navy surveillance vessel in a dangerous manner while it was on routine operations in international waters 75 miles (120km) south of Hainan island.
But China called the US complaint "totally inaccurate" and accused it of breaking international law by operating in its Exclusive Economic Zone (EEZ).
The US ship had behaved "like a spy" and China's action was "totally within our rights", state media quoted senior naval officials as saying.
The boundaries of China's EEZ remain disputed, while Beijing and Washington differ on which activities are permitted by law within a nation's EEZ. China has a key submarine base on Hainan island.
Speaking to reporters, Mrs Clinton also warned that Washington had "a range of options" it could take if North Korea goes ahead with a widely anticipated long-range missile test - including, Reuters reported, action in the UN Security Council.
She said the six-way talks on North Korea's nuclear programme would not be affected.
Mrs Clinton also expressed disappointment that a US special envoy who's just visited the region was not invited to Pyongyang.
North Korea insists it is preparing to launch a satellite, not a missile, and has said any attempt to shoot it down will result in war.
North Korea's nuclear programme, the global recession and the threat of climate change are among the issues likely to be covered in the US-Chinese talks.
Mr Yang was also due to meet Treasury Secretary Timothy Geithner on Wednesday, followed by President Obama on Thursday.