"I have no deadline, no," Trump told reporters in London, where he was due to attend a meeting of NATO leaders.
"In some ways, I like the idea of waiting until after the election for the China deal. But they want to make a deal now, and we'll see whether or not the deal's going to be right; it's got to be right."
European share prices and US stock futures fell, while the Chinese yuan currency sank to a five-week low on the comments by Trump, who has sought to increase trade pressure on other countries in the past 24 hours.
On Monday, he said he would hit Brazil and Argentina with trade tariffs for "massive devaluation of their currencies".
The United States then threatened duties of up to 100% on French goods because of a digital services tax that Washington says harms US tech companies.
Investors have been hoping that the United States and China can defuse their trade tensions, which have strained ties between the world's biggest and second-biggest economies since 2017, the first year of Trump's presidency.
Market jitters
US officials have previously said a deal could happen this year, depending on China.
The pan-European STOXX 600 index turned negative as Trump spoke, weighed down by export-heavy mining stocks.
"Each step back and each step forward is just part of a slow trend towards increased barriers to international trade," said Jonathan Bell, chief investment officer of Stanhope Capital.
"The market has taken an optimistic view so far this year on the likelihood of a successful outcome to trade negotiations. We worry that next year the market may turn back to looking more concerned."
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