President Donald Trump said Friday he has not agreed to rollback tariffs on Chinese imports, dampening recent optimism for a major de-escalation in the US-China trade war.

Trump's remarks appeared to push back against Beijing's claims this week that the two sides had agreed to remove tariffs in stages as part of a partial deal announced last month.

Hopes for progress in defusing trade tensions have driven global stocks higher this month. "They would like to have a rollback. I haven't agreed to anything," Trump told reporters at the White House. "China would like to get somewhat of a rollback, not a complete rollback, because they know I won't do it."

Beijing, however, said such this week the two sides had already agreed to mutual tariff reductions.

Chinese Commerce Ministry spokesman Gao Feng announced Thursday US and Chinese officials had "agreed to roll back the additional tariffs in stages, as progress is made towards a (final) agreement."

The United States and China have imposed steep tariffs on hundreds of billions of dollars in two-way trade, and another round of US duties are set to hit on December 15 on $160 billion in Chinese goods.

Trump again said Beijing is eager for a deal because their economy is hurting, although economic data show the conflict has hit US businesses as well, and the uncertainty over the dispute between the economic powers is undermining global growth.

"They would like to make a deal much more than I do," Trump said, adding that the initial agreement will be signed "in our country," possibly in Iowa.

Investors worldwide have been cheered in recent days by reports quoting sources in Washington and Beijing saying duties already imposed could be removed in a proportional way.

But markets also have been buffeted by conflicting comments from White House officials, including China hardliner Peter Navarro who earlier Friday cast doubt on any plans to remove punitive duties.

"What is on the table is tariffs coming in December, December 15," Peter Navarro told NPR radio. "We would be willing I think - it's up to the president - to postpone those tariffs."

"But not roll back any existing tariffs. That's the fine distinction here."

White House economic aide Larry Kudlow was less categorical, telling Bloomberg on Thursday that if the sides reach a phase one trade deal, "there are going to be tariff agreements and concessions."