Trump had been expected to order a so-called Section 301 investigation under the 1974 Trade Act earlier this month, but action had been postponed as the White House pressed for China's cooperation in reining in North Korea's nuclear program.
Trump said Friday that he planned to call Chinese President Xi Jinping that evening.
The trade investigation could strain relations between the US and China as the two countries wrestle with the unpredictable situation over North Korea. Speaking at a photo op at his Trump National Golf Club in Bedminster, New Jersey, Trump warned North Korea not to threaten the United States again or it would "face fire and fury like the world has never seen".
Alleged intellectual property theft by China has been an issue of particular concern to Silicon Valley.
It wasn't immediately clear how China would react to the move.
"We would like to emphasize that the Chinese government has always attached importance to intellectual property protection", a spokesman said.
Rubio said the nation is moving toward a big decision whether to live with a North Korea with the capability of striking the USA with a nuclear weapon. Russia's foreign minister, Sergey Lavrov, estimated the risk of a military conflict between the USA and North Korea as "very high", and said Moscow is deeply concerned. "They know how I feel", he told reporters on Thursday.
Rubio's defense of the President's comments is at odds with the opinions of some of his colleagues in the Senate - including Republicans - who criticized Trump for the harsh rhetoric.
Rubio was among many Republicans in the 2016 presidential primary and he and Trump had a heated and at times publicly contentious relationship past year.
"Protection measures against some specific items, such as steel and aluminum, may gain political favors, but are not likely to be of much help to rebalance trade", economists at the Institute of International Finance wrote in a research note this week.