"They'd like to have a roll back but I've not agreed to anything", Trump said.
Trump went on to explain that "China would like to get some kind of a rollback, not a complete rollback, because they know I won't do it".
The Chinese commerce ministry, without laying out a timetable, said the two countries had agreed to cancel the tariffs in phases.
White House officials speaking privately also confirmed the Chinese statement.
Trump said last month that the "Phase 1" pact would include the purchase of tens of billions of dollars of US farm products by China, which would benefit farm states, many of which supported Trump in 2016.
Financial markets in the US and globally rallied Thursday at the prospect of an agreement to wind down the U.S.
While the Trump administration has insisted that Americans are not bearing the brunt of the tariffs, business and farmer groups disagree.
A source previously told Reuters that Chinese negotiators wanted the United States to drop 15% tariffs on about $125 billion worth of Chinese goods that took effect on September 1. In return, the administration is demanding that Beijing agree to more extensive intellectual property safeguards, according to two people familiar with the talks.
The development suggests the two sides are moving closer to a deal that would provide relief to businesses and consumers that have struggled with the additional costs of tariffs.
Human built mammoth traps made 15,000 years ago discovered
Wooly mammoths , elephant-like creatures that once inhabited nearly every continent, became extinct about 4,000 years ago. The remains of species of horse and camel that disappeared from the Americas were also discovered at the site.
"By the day's end, Trump is the first bird of prey" on China exchange, said Whiton.
The official said China was believed to see a quick deal as its best chance for favorable terms, given pressure Trump is facing from a congressional impeachment inquiry as he seeks re-election in 2020.
HORSLEY: Still, White House officials remain cagey in committing to even a limited trade agreement. But the president said a formal text would soon be prepared.
"It makes a lot of sense politically and economically for the president to say this is enough", she said.
Four weeks later, the talks are shrouded in uncertainty.
A USA official confirmed the rollback would be part of the first phase of a trade agreement that is still being put to paper for Trump and President Xi Jinping to sign.
Trump hoped to hold it in the U.S. state of Iowa. That's lowered USA economic growth to 1.9% at an annual rate in the July-September quarter from 3.1% in the first three months of this year.
HORSLEY: In the meantime, the cost to the U.S. Friday's blizzard of contradictory remarks caused a modest dip in stock prices.
The tariff reduction was announced on Thursday on Chinese media and was not denied by the United States administration. A spokesperson for China's Commerce Ministry said that both parties need to undo the existing tariffs in the same proportion to reach phase one deal. "This is an important condition for reaching an agreement ..." -China trade relations and soaring USA crude oil inventories.
He said China wanted to make a deal more than he did, adding that the US tariffs were generating "billions" for USA coffers.