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BEIJING, July 4 (Reuters) - The Chinese commerce ministry said on Friday that Beijing and Washington had stepped up efforts to implement what they had agreed during recent trade talks but cautioned the U.S. against destabilising their "hard-won" consensus.

China hopes the U.S. can continue to meet it half way and maintain the stability of bilateral trade and economic relations, the commerce ministry said, as the two economic super-powers seek a resolution to their trade tensions.

"We hope the U.S. side will deeply understand the mutually beneficial and win-win nature of China-U.S. economic and trade relations," it said in a statement.

In three separate statements released in the past week about U.S. trade talks, the ministry called on Washington to preserve the positive momentum while also warning other countries against "making a deal at the expanse of China's interests" with the U.S.

Thanks to its trade truce with the U.S., China is not at risk of being slammed by higher tariffs when the 90-day pause on Liberation Day tariffs ends next week, but Trump's trade deals with Britain and Vietnam suggest China may remain an indirect target, said Julian Evans-Pritchard, head of China Economics.

"It seems that Trump is keen to crack down on the rerouting of Chinese exports via third countries, which has diminished the effectiveness of U.S. tariffs," Evans-Pritchard said.

As a July 9 trade deadline for countries to negotiate trade deals with the U.S. nears, Beijing is keen to remind Washington that the success of their trade talks in London did not come about easily.

Earlier this year, China retaliated against U.S. tariffs by suspending exports of a wide range of critical minerals and magnets. During U.S.-China trade talks in Geneva in May, Beijing committed to removing the measures imposed since April 2, but the U.S. said those critical materials were not moving as fast as agreed.

The breakthrough came during the London talks in June, with both sides agreeing for a framework to implement the Geneva agreement that involved expediting rare earth shipments to the U.S.

"China is currently reviewing and approving eligible export licence applications for controlled items," the commerce ministry said in the statement, referring to its own rare earth export curbs.

The U.S. has also taken actions "to lift a series of restrictive measures against China, and has informed China about the relevant situation," the ministry said, confirming reports that Washington resumed China-bound exports of chip design software, ethane and jet engines.

"Teams on both sides are stepping up efforts to implement relevant outcomes of the London Framework," the Chinese ministry said, calling the framework "hard-won".

Earlier this week, the U.S. sent letters to ethane producers to rescind a restrictive licensing requirement on exports to China imposed in late May and June, after its official confirmed concessions from Beijing over rare earths.

Some chip design software developers have restored access to their software and technology for customers in China after Washington lifted similar restrictions. GE Aerospace was also cleared to resume jet engine shipments to China.

(Reporting by Xiuhao Chen and Ryan Woo; Editing by Jamie Freed, Alexandra Hudson)

((Xiuhao.Chen@thomsonreuters.com;))