Mulino, after the talks with the top US diplomat in Panama City, signalled he would review agreements involving China and Chinese businesses, and announced further co-operation with the US on migration, but reiterated that his country's sovereignty over the world's second busiest waterway is not up for discussion.
Rubio delivered a message from Trump that China's presence - through a Hong Kong-based company operating two ports near the canal's entrances - was a threat to the waterway and a violation of the US-Panama treaty, US State Department spokesperson Tammy Bruce said in a statement.
Rubio did not spell out exactly what steps Panama must take or what US retaliation would look like.
Mulino indicated that he would review trade agreements involving China and Chinese businesses. (EPA PHOTO)
The Panama Canal serves as a vital trade route, connecting the Atlantic and Pacific Oceans and facilitating 40 per cent of US container traffic.
"We cannot allow any foreign power - particularly China - to hold that kind of potential control over it that they do," Rubio said. "That just can't continue."
Upon returning to office, Trump threatened to take control of the Panama Canal, built by the United States in the early 20th century and handed over to Panama in 1999, claiming the canal is being operated by Beijing.
He has refused to rule out use of military force over Panama, drawing criticism from Washington's Latin American friends and foes alike.
On Sunday, Trump said that he did not think troops would be necessary, but that Panama had violated the agreement and the United States would take back the canal.
"China's running the Panama Canal. That was not given to China, that was given to Panama - foolishly - but they violated the agreement, and we're going to take it back, or something very powerful is going to happen," Trump told reporters.
"I don't think troops will be necessary in Panama," he added.
Rubio (fourth from left) toured the Miraflores Locks at the Panama Canal during his visit. (AP PHOTO)
Rubio, a longtime China hawk during his Senate career, said last week on Sirius XM's The Megyn Kelly Show that China could use the ports to shut down the canal, a vital route for US shipping, in the event of a conflict between Beijing and Washington.
Mulino said his meeting with Rubio was respectful and cordial. He showed willingness to review some Chinese businesses in Panama, including a key 25-year concession to Hong Kong-based CK Hutchison Holdings, renewed in 2021 for the operation of ports at both entrances of the canal, pending the results of an audit.
Separately, Mulino suggested a possible expansion of an existing agreement with the United States from last July that could pave the way for direct deportations of non-Panamanian migrants who cross the Darien Gap jungle on Panama's southern border with Colombia.
He insisted, however, the US government would need to cover the cost.
"We spoke extensively about the problem of migration, with the understanding that Panama is a transit point," said Mulino, after his meeting with Rubio.
