Marco Rubio has told Panama’s president to immediately reduce what Donald Trump says is Chinese influence over the Panama Canal, or face potential retaliation from the United States.

On his first trip overseas as the top US diplomat, the US secretary of state took a guided tour of the canal accompanied by its Panamanian administrator as a South Korean-affiliated oil tanker and Marshall Islands-flagged cargo ship passed through the vital link between the Atlantic and Pacific oceans.

But Mr Rubio was said to have had a firmer message in private, telling Panama that Mr Trump had determined the country had violated terms of the treaty that handed over the canal at the end of 1999.

He pointed to the “influence and control” of China over the canal, through which some 40 per cent of US container traffic passes.

Meeting Jose Raul Mulino, Panama’s president, Mr Rubio “made clear that this status quo is unacceptable and that absent immediate changes, it would require the United States to take measures necessary to protect its rights under the treaty”, State Department spokeswoman Tammy Bruce said.

She did not spell out the consequences, but Mr Trump has repeatedly refused to rule out military force. On Saturday, he imposed punishing tariffs on the top US trading partners – Canada, China and Mexico.

Mr Mulino responded on Sunday by insisting he was not afraid of a US invasion and offered talks over the issue.