Additionally, the US and China will meet for a third day on Wednesday.
President Trump continues to be optimistic, tweeting the talks are going very well.
Lu Kang, spokesman for China's foreign ministry, said on Monday that Chinese military aircraft and naval vessels were dispatched to identify the USA vessel and warn it to leave the area near the disputed Paracel Islands in the South China Sea, claimed by China.
U.S. Commerce Secretary Wilbur Ross expressed optimism on Monday, telling CNBC that "there's a very good chance that we'll get a reasonable settlement".
People familiar with the talks said the world's two largest economies were further apart on Chinese structural reforms that the Trump administration is demanding in order to stop alleged theft and forced transfer of USA technology and on how to hold Beijing to its promises.
There was no immediate US response to the Chinese complaint. Liu led a previous round of talks in Washington a year ago that ended in failure, and he's expected to meet chief USA negotiator Robert Lighthizer later this month.
The U.S. negotiators in Beijing are pushing the Chinese side to come up with a mechanism to ensure that Beijing keeps the promises it makes, the Wall Street Journal reported.
The immediate trade issues would be easiest to tackle, while enforcement issues and structural reforms - such as intellectual property rights and market access - would be more challenging to resolve, he added. China responded by imposing penalties on $110 billion of American goods, slowing customs clearance for USA companies and suspending issuing licenses in finance and other businesses.
"Talks with China are going very well!" president Trump declared Tuesday, a day after the in-person talks in Beijing began with the participation of vice premier Liu and the US trade delegation.
Six months after Trump first slapped tariffs on Chinese goods, signs are growing that the trade war is exacting an economic and financial cost, increasing the incentive for both sides to end the conflict. "We have firm confidence in the strong long-term fundamentals of the Chinese economy".
After months of US tariffs on Chinese imports and Chinese retaliatory tariffs on USA goods, Trump and Chinese President Xi Jinping held December 1, 2018 meetings at the G20 in Argentina. More senior-level discussions could take place this month, with the South China Morning Post reporting that Trump and Chinese Vice President Wang Qishan may meet at the World Economic Forum in Davos, Switzerland.
The talks went ahead despite tensions over the arrest of a Chinese tech executive in Canada on US charges related to possible violations of trade sanctions against Iran.
The White House is making sure this go-around is different.
The U.S. trade delegation includes Deputy U.S. Trade Representative Ambassador Jeffrey Gerrish, USTR Chief Agricultural Negotiator Ambassador Gregg Doud, Under Secretary for Trade and Foreign Agricultural Affairs Ted McKinney, Under Secretary of Commerce for International Trade Gilbert B. Kaplan, Assistant Secretary for Fossil Energy Steven Winberg, and Under Secretary for International Affairs David Malpass.