Trump has imposed tariffs on $250 billion (£194.8 billion) of Chinese imports to force concessions from Beijing on the list of demands that would change the terms of trade between the two countries. China has responded with import tariffs on U.S. goods.
Washington is demanding Beijing improve market access and intellectual property protections for U.S. companies, cut industrial subsidies and slash a $375 billion trade gap.
The relationship between the two countries has deteriorated in recent months, and U.S. Vice President Mike Pence on Tuesday said China needed to change its behaviour to avoid a new cold war with the United States.
The U.S. tariff rate on $200 billion in Chinese goods is set to increase to 25 percent from 10 percent on Jan. 1. Trump has threatened to impose tariffs on all remaining Chinese imports - about $267 billion more in goods - if Beijing fails to address U.S. demands.
"We may not have to do that," Trump told reporters at the White House. "China would like to make a deal.
But Trump added that there were "four or five big things left off" the list of 142 items sent by China.
"They sent a list of things that they're willing to do, which is a large list, and it's just not acceptable to me yet." he said. He did not detail the omitted items.
Trump said, however, he was confident the missing items would be addressed in any deal struck with China.
"I think we'll probably get them too," he said.
Trump's softening line on tariffs gave a modest lift to stocks.
Trump is expected to meet Chinese President Xi Jinping on the sidelines of a G20 summit in Argentina later this month.
Officials have played down the probability that the two will make a deal to end their trade war at the meeting. One source briefed on the offer said it was just a "rehash" of previous offers China had made.
But if Trump holds fire on further tariffs, the Chinese offer may have contained enough for Washington to engage fully in negotiations for a deal.
The United States had said it would not restart negotiations on a trade deal until it saw a concrete response to China on its demands, although informal talks between the two on trade restarted earlier this month after Trump and Xi talked via telephone.
Reuters reported this week that China sent the written response to U.S. demands on Monday, ending a months-long wait.
The Chinese document included 142 items divided into three categories: issues China was willing to negotiate for further action, issues it was already working on and issues considered off limits, a U.S. official told Reuters on Thursday.
Trump's team of economic advisers have voiced conflicting views on doing a deal with China. Some, such trade adviser as Peter Navarro, advocate taking a hard line on trade until China makes deep economic forms.
Others, such as economic adviser Larry Kudlow, want to see reforms but have pressed for a deal to avoid further disruption to trade between the world's two largest economies. - Reuters
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