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* Mnuchin says China, U.S. hold "productive" talks in Beijing
* Chinese vice premier due in Washington next week
* Two countries trying to end bitter trade war (Adds Chinese state media)
BEIJING, May 1 (Reuters) - China and the United States held "productive" trade talks in Beijing on Wednesday and will continue discussions in Washington next week, U.S. Treasury Secretary Steven Mnuchin said, as the two try to end their trade war.
Mnuchin, along with U.S. Trade Representative Robert Lighthizer, held a day of discussions, before Chinese Vice Premier Liu He goes to Washington next week for another round of talks in what could be the end game for negotiations.
"Ambassador Lighthizer and I just concluded productive meetings with China's Vice Premier Liu He. We will continue our talks in Washington, D.C. next week," Mnuchin wrote on his Twitter account. He gave no details.
The three men appeared before cameras at the end of their talks at a state guest house in Beijing, chatting amiably amongst themselves but did not speak to reporters.
China's official Xinhua news agency, in a brief report, simply noted that the latest talks had taken place and that the next rounds of talks would take place in Washington next week as planned.
Liu had entertained his U.S. guests on Tuesday night just after they arrived in the Chinese capital.
"We did. We had a nice working dinner, thank you," Mnuchin told reporters at his Beijing hotel earlier on Wednesday, when asked if he had met with Liu on Tuesday. He did not elaborate.
Beijing and Washington have cited progress on issues including intellectual property and forced technology transfer to help end a conflict marked by tit-for-tat tariffs that have cost both sides billions of dollars, disrupted supply chains and roiled financial markets.
But U.S. officials say privately that an enforcement mechanism for a deal and timelines for lifting tariffs are sticking points.
Chinese officials have also acknowledged that they view the enforcement mechanism as crucial, but say that it must work two ways and cannot put restraints only on China.
In Washington, people familiar with the talks say that the question of whether and when U.S. tariffs on $250 billion worth of Chinese goods will be removed will probably be among the last issues to be resolved.
U.S. President Donald Trump has said that he may keep some tariffs on Chinese goods for a "substantial period".
The United States has also been pressing China to further open up its market to U.S. firms. China has repeatedly pledged to continue reforms and make it easier for foreign companies to operate in the country.
In comments published in Wednesday, China's top banking and insurance regulator said the government would further open up its banking and insurance sectors. (Reporting by Tom Daly and Ben Blanchard; Editing by Simon Cameron-Moore and Jon Boyle)