Trump on Saturday ordered sweeping tariffs on goods from Mexico, Canada and China, as part of demands they stop the flow of illegal fentanyl.
On Monday, Trump threatened to ramp up tariffs on China further, which were set at 10 per cent on goods from that country, along with 25 per cent tariffs on Mexican and most Canadian imports, starting on Tuesday. He later paused the levies on Mexico after the country promised to reinforce its border with the United States.
But those tariffs stopped short of Trump's campaign promises for vast new tariffs on Chinese goods, and on Monday he described the initial tranche as an "opening salvo."
"China hopefully is going to stop sending us fentanyl, and if they're not, the tariffs are going to go substantially higher," Trump said.
"China will be dealt with," he added.
Trump also repeated his opposition to Chinese involvement in logistics at the Panama Canal, a major trade crossing in the Americas.
"China's involved with the Panama Canal. They won't be for long," Trump told reporters in the Oval Office.
China's UN ambassador Fu Cong rejected accusations of Beijing managing the Panama Canal. (AP PHOTO)
On Monday, China categorically rejected US accusations of its alleged influence over the canal.
"Let me say that I think the accusation against China is totally false," China's UN ambassador Fu Cong said in New York.
"Let me emphasise that China has not participated in the management and operation of Panama Canal and has never interfered in canal affairs," he added.
China respects Panama's sovereignty over the canal and recognises it as a permanent neutral international gateway, Fu said.
If Panama were to reduce its co-operation with China as part of the Belt and Road Initiative under pressure from the United States, this would be an "regrettable decision," the ambassador warned.
Separately, Fu said a United Nations Security Council meeting in two weeks could be a "very good opportunity" for Chinese Foreign Minister Wang Yi and US Secretary of State Marco Rubio to meet.
China is president of the Security Council for February and Fu said Wang would chair a ministerial meeting of the 15-member body on February 18 that would focus on multilateralism and improving global governance.
The US State Department did not immediately respond to a request for comment on whether Rubio would attend the meeting. Rubio and Wang have spoken on the phone.
"I do hope that despite all the rhetoric that we have heard from the American politicians, we can take a constructive and - I will emphasise - a professional approach to our work here in the United Nations," Fu told reporters. "So much is at stake."
with DPA