Trump said the postponement came "at the request of the Vice Premier of China, Liu He, and due to the fact that the People's Republic of China will be celebrating their 70th Anniversary."
The tariffs were set to increase to 30 percent from 25 percent on the goods.
Chinese trade deputies are expected to meet their US counterparts in mid-September in Washington before ministerail meetings in early October in the US capital, involving Chinese Vice Premier Liu He, US Trade Representative Robert Lighthizer and US Treasury Secretary Steven Mnuchin.
The delay could enable talks to take place before the tariffs kick in.
On Wednesday, Trump also said that he welcomed China's decision to exempt some US anti-cancer drugs and other goods from its tariffs.
Stock markets in Asia rose on the news in early Thursday trade, as the concessions came days before a planned meeting aimed at defusing the escalating trade war between the world's two largest economies.
China's decision to exempt some US goods was a "big move" by Beijing and a positive gesture before trade negotiators from both countries meet in Washington, Trump told reporters at the White House.
China on Wednesday announced its first batch of tariff exemptions for 16 types of US products, including some anti-cancer drugs and lubricants, as well as animal feed ingredients whey and fish meal, according to a Ministry of Finance statement on its website.
"They made a couple of moves ... that were pretty good," Trump said at an unrelated event on vaping. "I think it was a gesture, okay? But it was a big move."
Trump said he hoped to reach a trade agreement with China following more than a year of tit-for-tat exchanges of tariffs that have roiled global markets.
"I deal with them and I know them and I like them," he said. "I hope we can do something."
Asian stocks rose on Thursday, while China's yuan currency was also up 0.27 percent in offshore trade, as investors hoped for a thaw in US-China trade frictions.
The gestures may ease tensions in advance of the negotiations, but some analysts don't see it as a signal that both sides are getting ready for a deal.
"The exemption could be seen as a gesture of sincerity towards the US in the run-up to negotiations in October but is probably more a means of supporting the economy," ING's Greater China economist Iris Pang wrote in a note.
"There are still many uncertainties in the coming trade talks. An exemption list of just 16 items will not change China's stance," she said.
Indeed, the exempted list pales in comparison to over 5,000 types of US products that are already subject to China's additional tariffs. Moreover, major US imports, such as soybeans and pork, are still subject to hefty additional duties, as China has ramped up imports from Brazil and other supplying countries.
Beijing has said it would work on exempting some US products from tariffs if they are not easily substituted from elsewhere. The US is by far China's largest supplier of whey, which is an important ingredient in piglet feed and difficult to source in large volumes from elsewhere.
Analysts say that with its duties on soybeans and US-made cars, China is taking aim at a key political support base of Trump, mainly at the factories and farms across the Midwest and South just when there's receding momentum in the world's top economy.
In all, the US and China have slapped tariffs on hundreds of billions of dollars worth of goods in a bitter trade war that has raised the spectre of a global recession, with further tariffs slated to take effect in coming months.
Key US officials are tamping down expectations for a major accord.
Senior White House adviser Peter Navarro this week urged investors, businesses and the public to be patient about the trade dispute.
Earlier on Wednesday, a survey by a prominent American business association showed the trade dispute was souring the profit and investment outlook for US companies operating in the world's second-biggest economy.