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China has declined to confirm President Trump's announcement, which he made on Twitter without providing details.
The move, if confirmed, would be welcomed by a car industry unsettled by the escalating US-China trade war.
President Trump and Xi Jinping have now agreed to a temporary truce in the bitter dispute.
Over dinner at the G20 summit, they agreed to not increase tariffs for 90 days to allow for talks.
Failure to strike a deal would have seen tariffs on $200bn worth of Chinese goods rise from 10% to 25% at the start of next year, and would have opened the way for tariffs on additional Chinese goods.
President Trump was in ebullient mood after the developments.
On Monday, China's foreign ministry said the presidents of China and the US had instructed their economic teams to "intensify talks" towards removing all tariffs following the G20 meeting, However, it did not say if that was a plan with specific goals or something that was merely desirable.
Asian markets rallied after news of the trade war truce. In China, Hong Kong's Hang Seng index climbed 2.5% and the Shanghai Composite index jumped 2.6%. Japan's Nikkei 225 index rose 1%.
The gains spread to Europe, with the UK's FTSE 100 index, the Cac 40 in France and Germany's Dax index all up by about 2%.
The trade war has seen the US and China hit each other with escalating tariffs in an attempt to make their domestically made goods more competitive.
The US says its tariff policy is a response to China's "unfair" trade practices and accuses it of intellectual property theft.
Since July, the US has hit China with tariffs on $250bn (£195.9bn) worth of goods. China has retaliated with duties on some $110bn of US goods over the same period.
As part of this, the US imposed a 25% tariff on Chinese cars, on top of the 2.5% already in place.
In July, China, which is the world's largest market for cars, imposed a 40% tariff on US vehicle imports. The rate is much higher than the 15% it places on other trading partners and forced many carmakers to raise prices.
In his tweet, President Trump said Beijing had "agreed to reduce and remove tariffs on cars coming into China from the US".
He did not provide a new level for the Chinese tariffs, and Beijing did not immediately confirm the statement.
What was agreed at the G20?
In a statement, the White House said US tariffs on Chinese goods would remain unchanged for 90 days, but added: "If at the end of this period of time, the parties are unable to reach an agreement, the 10 percent tariffs will be raised to 25 percent."
The US manufactures cars for export to China, the world's largest car market
The US said China agreed to "purchase a not yet agreed upon, but very substantial, amount of agricultural, energy, industrial, and other products from the United States to reduce the trade imbalance between our two countries".
Both sides also pledged to "immediately begin negotiations on structural changes with respect to forced technology transfer, intellectual property protection, non-tariff barriers, cyber intrusions and cyber theft", according to the White House.
Chinese Foreign Minister Wang Yi told reporters after the talks that "the principal agreement has effectively prevented further expansion of economic friction between the two countries".
Are tariffs still in place?
Yes. The truce prevents raising tariffs as planned on $200bn worth of Chinese goods.
But it does not remove tariffs that apply to a total of $250bn of Chinese goods targeted since July.
The truce also does not affect the existing duties China has imposed on $110bn of US goods in a tit for tat retaliation.
Will this resolve the dispute?
While the result of the G20 meeting was better than expected, it is unclear how the two countries will manage to resolve their underlying differences.
"There should be no wishful thinking that the truce would end the trade war between the world's two largest economies," DBS strategist Philip Wee wrote in a research note.
He said it "remains to be seen if real progress could be achieved during this narrow window to resolve the contentious issues, not just on trade, but also intellectual property".
Louis Kuijs, head of Asia economics at Oxford Economics, said while the agreement itself was "positive" the next steps remained unclear.
"Whether we will see further de-escalation or whether it is temporary reprieve continues to be very much up to a political decision in Washington DC - that will continue to make this uncertain," Louis Kuijs, head of Asia economics at Oxford Economics said.
