The White House did not immediately say what authority the President had to compel private firms to quit a country, the BBC reported on Friday.
The US President also vowed swift retaliation against Beijing after it unveiled plans for duties of 10 per cent on $75 billion of US goods.
The latest salvos in the trade war sent global financial markets tumbling.
The Dow Jones Industrial Average lost more than 620 points, or 2.4 per cent, while London's FTSE 100 and the German DAX also turned negative.
In a blistering Twitter screed on Friday, Trump said: "Our great American companies are hereby ordered to immediately start looking for an alternative to China, including bringing... your companies HOME and making your products in the USA."
He also tweeted: "We don't need China and, frankly, would be far... better off without them.
"Our Country has lost, stupidly, Trillions of Dollars with China over many years. They have stolen our Intellectual Property at a rate of Hundreds of Billions of Dollars a year, & they want to continue. I won't let that happen!
China's new tariffs will range between 5 per cent and 10 per cent and apply to more than 5,000 goods coming from the US.
Agricultural goods, crude oil and small aircraft are among the targeted items.
On Friday, Trump tweeted that he would be "responding to China's Tariffs this afternoon".
"This is a GREAT opportunity for the United States," he wrote.
Beijing also said it will revive a 25 per cent tariff on US car imports that it lifted earlier in 2019 in a goodwill gesture as the two countries tried to negotiate a trade agreement.
Carmakers warned that the tax would put US jobs at risk.
"When these tariffs were initially imposed by China in 2017, American exports of finished vehicles dropped by 50 per cent," said John Bozzella, who represents car manufacturers.
"We can't let that happen to American workers again."
On August 1, President Trump unveiled a 10 per cent tariff on $300 billion of Chinese goods, blaming China for not following through on promises to buy more American agricultural products.
That tariff was expected to be introduced on September 1, but less than two weeks later, Trump delayed that date to December 15, partly due to concerns it might hit Christmas shoppers.
China said it planned to impose its new tariffs in two stages on September 1 and December 15.
( With inputs from IANS )