"China will take down its trade barriers because it is the right thing to do," Trump said in a tweet.
"Taxes will become reciprocal & deal will be made on Intellectual Property. Great future for both countries!"
He added that he and China's President Xi Jinping "will always be friends, no matter what happens with our dispute on trade."
US stocks plunged more than two percent Friday after Trump warned of tariffs on an additional $100 billion worth of Chinese imports, provoking a strong response from Beijing and fanning fears of a full-blown trade war.
Investors were unnerved by the latest broadside from the volatile US president and by the strident response from China, which vowed to stand firm "until the end at any cost."
Some global investors have, however, taken solace from signals that the Trump administration may be taking a harsh line as a bargaining tactic towards dealmaking with China.
In the wake of Trump's decision in March to impose steep tariffs on steel and aluminum imports, primarily to target China, the US on Tuesday published a list of $50 billion in Chinese goods to be hit by tariffs over what Washington says is widespread theft of intellectual property and technology.
China retaliated by unveiling planned levies on $50 billion worth of major US exports including soybeans, cars and small aircraft.
Trump hit back again late Thursday, instructing trade officials to consider the additional levies on $100 billion in imports.
Dismissing trade war talk
"Rather than remedy its misconduct, China has chosen to harm our farmers and manufacturers," Trump said at the time, calling Beijing's reaction "unfair."
So far, only the tariffs on steel and aluminum have taken effect.
US businesses, and farm states most vulnerable to Chinese retaliation, have called for restraint.
Trump's senior economic advisers on Sunday dismissed talk of a trade war and said the president is serious about imposing tariffs, even as talks continue with China.
"We do have constant communication with them," chief economic adviser Larry Kudlow said on "Fox News Sunday."
"But in this process tariffs have to be part of it, there's no two ways about it. Then, hopefully, there will be discussions, and hopefully in just the next two months the Chinese will come seriously back to the table."
Another adviser, Peter Navarro, told NBC's "Meet the Press" that while "there are discussions" with the Chinese, the US is moving forward on tariffs and investment restrictions against Beijing.
"We want fair and reciprocal trade. We want them to stop stealing our stuff. We want 'em to guard intellectual property, not take it from us."
Asked on CBS's "Face the Nation" about Trump's Sunday tweets and whether China has given any sign of concessions, Treasury Secretary Steven Mnuchin said "it would be inappropriate for me to comment on what our back-channel discussions are."
He said he did not think there will be a trade war.
Trump "has a very close relationship with President Xi and we'll continue to discuss these issues with them," Mnuchin said.
