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* U.S. officials in Beijing for latest round of trade talks
* Mnuchin says hopes to make "substantial progress"
* Senior Chinese diplomat says talks have achieved progress
* Chinese vice premier due in Washington next week (Adds comments by senior Chinese diplomat, byline)
BEIJING, April 30 (Reuters) - U.S. Treasury Secretary Steven Mnuchin said on Tuesday that he hopes to make "substantial progress" with Chinese negotiators in the next two rounds of trade talks, as the world's two largest economies look for ways to end their bruising trade war.
Mnuchin was speaking in Beijing, where he and U.S. Trade Representative Robert Lighthizer will hold talks this week, 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.
"We've a meeting here, and then the vice premier and team will be coming back to Washington D.C., and we hope to make substantial progress in these two meetings," Mnuchin told reporters.
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.
"I'm not going to comment on specific issues of the discussions," Mnuchin said. "They've been quite broad as I've said before. We've made a lot of progress. We look forward to the meetings here."
At a separate meeting on Tuesday, with a group of former U.S. lawmakers, the Chinese government's top diplomat, State Councillor Wang Yi, said the two countries' interests were deeply connected.
"In recent months, both countries' economic and trade teams have held many rounds of high-level consultations and achieved much positive progress," China's Foreign Ministry paraphrased Wang as saying.
China hopes that both sides can "work hard, exclude disturbances, and reach a mutually beneficial, win-win agreement", he added.
Chinese officials have also acknowledged that they view the enforcement mechanism as crucial, but that it can't only put restraints on China.
"There must be guarantees for implementation. This is an important part of the negotiations. We must, to the greatest extent possible, lower and prevent the chances of going back on promises," one Chinese official close to senior leaders told Reuters.
A second Chinese official with knowledge of the situation said it was too early to say work was in the final stages, but that both sides were "sprinting".
U.S. President Donald Trump said on April 4 that a deal might be worked out in about four weeks. Last week, he said he would soon host Chinese President Xi Jinping at the White House. A meeting between the two leaders is seen as needed to cement an agreement.
Mnuchin, speaking to Fox Business Network in an interview that aired on Monday, said the trade negotiations aimed at enforcement were close to finished.
China's foreign ministry said at its daily press briefing that substantive progress had been made on the talks but gave no details.
(Reporting by Ben Blanchard; Additional reporting by Michael Martina and Xu Jing; writing by Se Young Lee and Ryan Woo; Editing by Simon Cameron-Moore and Nick Macfie)