Trump made the remarks after two days of high-level negotiations broke up in Beijing Friday, and the two countries announced plans to resume talks next week in Washington. The world's two biggest economies are locked in a dispute over China's aggressive push to challenge American technological dominance.
The U.S. is scheduled to hike import taxes on $200 billion worth of Chinese goods on March 2. But Trump told reporters that he might extend the deadline "if I see that we're close to a deal or the deal is going in the right direction." He had made similar comments on Tuesday.
Earlier Friday, U.S. Trade Representative Robert Lighthizer told Chinese President Xi Jinping negotiators "made headway" in talks this week in Beijing.
Economists said this week's two days of talks were too brief to resolve the sprawling dispute that extends to cyber-spying and China's trade surplus. They said Beijing is trying to persuade Trump enough progress is being made to postpone the penalties.
. "I hope you will continue to work hard to promote a mutually beneficial and win-win agreement," Chinese President Xi Jinping told Lighthizer in a meeting after the negotiations ended, according to the official Xinhua News Agency.
The decision to hold more talks suggested they were making progress. But there was no indication of movement on the thorniest dispute: U.S. pressure on Beijing to scale back plans for government-led creation of Chinese global leaders in robotics and other technologies.
"We feel we have made headway on very, very important and difficult issues," Lighthizer told Xi. "We have additional work we have to do but we are hopeful."
Xi said Beijing and Washington "share broad mutual interests" in promoting global economic prosperity and stability.
"We shoulder important responsibilities," the Chinese leader said.
Washington, Europe, Japan and other governments say Beijing's industry plans violate its market-opening obligations. Some American officials worry they might erode U.S. industrial leadership.
Trump raised tariffs in July over complaints Beijing steals or pressures companies to hand over technology. He imposed 25 percent penalties on $50 billion of goods from China and 10 percent on $200 billion.
China retaliated by raising duties on American soybeans and other imports and ordering its companies to find other suppliers. Imports of American goods plunged 41.2 percent in January compared with a year earlier, according to customs data.
Trump agreed Dec. 1 to postpone further penalties by 90 days while the two sides negotiate. Once that expires March 1, the charges on $200 billion of goods are due to rise to 25 percent.
Both governments face growing pressure to make peace as global economic growth weakens and the cost to their companies increases.
Beijing has offered to narrow its trade surplus by purchasing more American soybeans, natural gas and other exports. But the government has resisted pressure to cut back development plans it sees as a path to prosperity and global influence.
"From politics to economy to ideology, the United States hopes to intervene in China's affairs," said the newspaper Global Times, published by the ruling Communist Party.
Companies on both sides have been battered by penalties. Foreign manufacturers in China are starting to shift production of goods bound for the U.S. market to other countries to avoid Trump's tariffs, suggesting they anticipate an extended conflict.
A possible sticking point is Chinese reluctance to agree to an enforcement mechanism demanded by American officials to monitor whether Beijing carries out its promises.
Beijing has tried to deflect pressure by emphasizing China's growth as an export market. It has announced changes over the past year to open finance and other fields, including allowing full foreign ownership in its auto industry for the first time.
The U.S. delegation also included Treasury Secretary Steven Mnuchin and David Malpass, a Treasury undersecretary who is Trump's nominee for World Bank president.
The Chinese delegation was led by Vice Premier Liu He, Xi's chief economic adviser.
Chinese regulators also have announced plans to improve protection of foreign patents and copyrights.
It is unclear whether that will satisfy Washington and other governments that complain the system is rigged to extract technology from foreign companies and to use official industrial standards to shield Chinese enterprises from competition.
Darlene Superville in Washington contributed to this story.