Panama has complained to the United Nations over US President Donald Trump's "worrying" threat to seize the Panama Canal, even as it launched an audit of the Hong Kong-linked operator of two ports on the interoceanic waterway.

Trump, in his inaugural address Monday, repeated his complaint that China was effectively "operating" the Panama Canal through its growing presence around the waterway.

Panama's president has rejected a plan by Donald Trump to "take back" the Panama Canal, telling his US counterpart the key trade route "is and will remain" in the country's hands. In his inaugural speech, President Trump claimed that Panama had "broken" a promise to remain neutral, alleging that "China is operating the Panama Canal".