The Australian dollar gained 0.4 percent to $0.7157, reacting to Trump's latest posts on Twitter.
The offshore yuan strengthened 0.3 percent to 6.6806 yuan against the dollar, its highest level since mid-July, also on the news he will not raise tariffs on $200 billion of Chinese imports to 25 percent from 10 percent.
The Japanese yen eased 0.1 percent to 110.75 yen to the dollar, while the euro gained 0.1 percent to $1.1346.
The dollar index against a basket of six major currencies barely moved and was at 96.446.
The U.S. president also said he would plan a summit meeting with Chinese President Xi Jinping at his Mar-a-Lago estate in Florida to conclude an agreement, assuming the trade talks make additional progress.
Trump's delay of higher tariffs "didn't come as a total surprise," said Shinichiro Kadota, senior forex and rates strategist at Barclays in Tokyo. "So I expect the market reaction should be somewhat limited and that the focus would shift back to global economic fundamentals."
Indeed, Trump's tweets came amid rising expectations that he would delay increasing higher tariffs before the March 1 deadline to avoid escalating the U.S.-China trade war.
The president said in a tweet that progress had been made on a host of divisive areas including intellectual property protection, technology transfers, agriculture, services and currency.
Elsewhere, the New Zealand dollar rose 0.5 percent to $0.6875, also helped by local retail sales jumped in the fourth quarter, tempering concerns of softer growth in the country's economy.
The British pound was idling at $1.3067 as markets awaited some clarity on where Brexit talks were heading.
Prime Minister Theresa May put off a vote on her Brexit deal until as late as March 12 - just 17 days before Britain is due to leave the EU - setting up a showdown this week with lawmakers who accuse her of running out the clock.
The Telegraph reported that May was considering whether to delay Britain's exit for up to two months.