WASHINGTON/NEW YORK (Reuters) - U.S. and Chinese trade officials held a “constructive” phone conversation on Tuesday, White House economic adviser Larry Kudlow said, marking a new round of talks after the world’s two largest economies agreed to a truce in a year-long trade war.

FILE PHOTO: White House chief economic adviser Larry Kudlow speaks with reporters on the driveway outside the West Wing in Washington, U.S. June 18, 2019. REUTERS/Jonathan Ernst/File Photo

U.S. Trade Representative Robert Lighthizer and Treasury Secretary Steven Mnuchin spoke with Chinese Vice Premier Liu He and Commerce Minister Zhong Shan on Tuesday in a further effort to resolve outstanding trade disputes between the countries, a U.S. official said earlier in an emailed statement.

Kudlow said the talks “went well” and were constructive. He said the two sides were talking about a face-to-face meeting, but warned that there was not a magic way to reach what has so far been an elusive deal.

“There are no miracles here,” Kudlow told reporters at the White House. “There was headway last winter and spring, then it stopped. Hopefully we can pick up where we left off, but I don’t know that yet.”

China’s Commerce Ministry said in a short statement that the two sides had “exchanged views on implementing the consensus of the two countries’ leaders at the Osaka meeting”. It gave no other details.

The United States and China agreed during a Group of 20 nations summit in Japan last month to resume discussions, easing fears of an escalation. After meeting with Chinese President Xi Jinping at the G20, U.S. President Donald Trump agreed to suspend a new round of tariffs on $300 billion worth of imported Chinese consumer goods while the two sides resumed negotiations.

Trade talks stalled in May after China backed away from commitments it had made to secure legal changes to its system, according to U.S. officials.

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Kudlow’s comments suggested it was still unclear whether the two sides would resume work from the draft text agreed before that pull-back, as U.S. officials want, or whether they will use a different starting point.

A face-to-face meeting between the two negotiating teams would be a good thing and could take place in Beijing, Kudlow said, but no details were available yet.

“Both sides will continue these talks as appropriate,” the separate U.S. official said in an email, declining to provide details on what was discussed and the next steps for talks.

The negotiations picked up after a two-month hiatus, but a year since a tit-for-tat tariff battle began between the two countries. Washington wants Beijing to address what U.S. officials see as decades of unfair and illegal trading practices.

Trump said in Osaka that China would restart large purchases of U.S. agricultural commodities, and the United States would ease some export restrictions on Chinese telecom equipment giant Huawei Technologies.

“President Xi is expected, we hope in return for our accommodations, to move immediately, quickly, while the talks are going on, on the agriculture (purchases),” Kudlow said on Tuesday at an event hosted by CNBC. “That’s very, very important.”

He also said relaxed U.S. government restrictions on Huawei could help the technology giant but would only be in place for a limited time.

Kudlow, the director of the White House’s National Economic Council, later told reporters there was no specific timeline for the agricultural buys, or for reaching an agreement. “No timeline. Quality not speed,” he added.

Three sources familiar with the state of the talks said the Chinese side did not make firm commitments for immediate purchases. It’s unclear that the two sides’ differences have narrowed, even as the discussions resume.

(This July 9 story has been refiled to correct formal title of Zhong Shan to Commerce Minister, not Trade Minister, in second paragraph.)