China and the U.S. have agreed to roll back tariffs on each other’s goods in phases as they work toward a deal between the two sides, a Ministry of Commerce spokesman said.

“In the past two weeks, top negotiators had serious, constructive discussions and agreed to remove the additional tariffs in phases as progress is made on the agreement,” spokesman Gao Feng said Thursday.

A U.S. official, who spoke on condition of anonymity, confirmed Thursday that an agreement to roll back tariffs would be part of phase-one deal. The negotiations are ongoing and a time or place for any signing of a pact is yet to be determined.

Kellyanne Conway, senior White House adviser, said Thursday that President Donald Trump is "anxious" to sign the deal.

“If China, U.S. reach a phase-one deal, both sides should roll back existing additional tariffs in the same proportion simultaneously based on the content of the agreement, which is an important condition for reaching the agreement,” Gao said.

Such an understanding could help provide a road-map to a deal de-escalating the trade war that’s cast a shadow over the world economy. China’s key demand since the start of negotiations has been the removal of punitive tariffs imposed by Trump, which by now apply to the majority of its exports to the U.S.

Stocks rallied, with Hong Kong’s Hang Seng Index climbing 0.6%. European and U.S. shares rose. The yuan strengthened.

“The question right now is what the two sides have actually agreed on -- the market’s focus has shifted to how the U.S. may react to China’s tariff remarks tonight or in coming days,” said Tommy Xie, an economist at Oversea-Chinese Banking Corp. “Investors are still cautious.”

The two sides continue to negotiate over where and when a “Phase One” deal would be signed. Gao said he had no further information on the location or timing.

U.S. locations for a Trump-Xi meeting that had been proposed by the White House, including Iowa and Alaska, have been ruled out, according to a person familiar with the matter. Locations in Asia and Europe are now being considered instead, the person said, asking not to be identified because the discussions aren’t public.

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