Panama City, Panama - US Secretary of State Marco Rubio on Sunday threatened action against Panama without immediate changes to reduce Chinese influence on the canal, but the country's leader insisted he was not afraid of a US invasion and offered talks.

Rubio, paying his first visit overseas as the top US diplomat, told Panama that President Donald Trump had determined that the country had violated terms of the treaty that handed back the crucial waterway in 1999.

He pointed to the "influence and control" of China over the canal, the vital link between the Atlantic and Pacific oceans through which some 40% of US container traffic passes.

Meeting President Jose Raul Mulino, 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.

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Mulino painted a less dire portrait of the meeting. He welcomed Rubio at his official residence in the tropical capital's old quarter, with an honor guard outside the whitewashed walls.

"I don't feel that there is any real threat at this time against the treaty, its validity, or much less of the use of military force to seize the canal," Mulino told reporters afterward, referring to the treaty that handed over the canal at the end of 1999.

"Sovereignty over the canal is not in question," Mulino said.

He proposed technical-level talks with the US to clear up concerns.

Rubio did not spell out what measures the US may take. Trump in recent days has imposed hefty tariffs on the three biggest trading partners of the US – Canada, China, and Mexico.

Rubio and Trump say that China has gained so much power around surrounding infrastructure that it could shut it down in a potential conflict, with catastrophic consequences for the US.

Small but intense protests broke out in Panama ahead of Rubio's visit, with police firing tear gas.

Protesters burned an effigy of Rubio wearing a red, white, and blue suit and held up pictures of him and Trump before a Nazi flag.

"Rubio, get out of Panama!" around 200 demonstrators chanted as the former senator met Mulino. Police prevented the crowd from approaching the Old City.

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"To the imperial messenger," union leader Saul Mendez said of Rubio, "we reiterate that there is absolutely nothing here for Trump. Panama is a free and sovereign nation."

Mulino, in response to pressure, ordered an audit of a Hong Kong-based company that controls ports on both sides of the canal.

But speaking to reporters on Friday, Trump said that concession was not enough on the canal and that "it's appropriate that we take it back."

Rubio, the first Hispanic secretary of state and a devout Catholic, started his Sunday in Panama City attending Mass at a church built four centuries ago in the Old City.

He will travel to four more Latin American countries – El Salvador, Costa Rica, Guatemala, and the Dominican Republic – where he is expected to press for cooperation on Trump's key priority of deporting migrants from the US.