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 inter-oceanic waterway.

In a letter to UN Secretary-General Antonio Guterres, the government in Panama City referred to an article of the UN Charter precluding any member from "the threat or use of force" against the territorial integrity or political independence of another.

The missive distributed to reporters on Tuesday urges Guterres to refer the matter to the UN Security Council, without asking for a meeting to be convened.

Trump, in his inaugural address on Monday, repeated his complaint that China was effectively "operating" the Panama Canal through its growing presence around the waterway, which the United States handed over at the end of 1999.

"We didn't give it to China, we gave it to Panama. And we're taking it back," Trump said.

The Panamanian comptroller's office that oversees public entities then announced an "exhaustive audit" would be launched to ensure the "efficient and transparent use of public resources" at the Panama Ports Company.

The company, part of Hutchison Ports, a subsidiary of Hong Kong-based conglomerate CK Hutchison Holdings, operates the ports of Balboa and Cristobal on either end of the canal.

The comptroller's office said the aim was to determine whether the company was complying with its concession agreements, including adequate reporting of income, payments and contributions to the state.

Panama's President Jose Raul Mulino has denied that any other nation was interfering in the canal, which he said operated on the principle of neutrality.

"The canal is and will remain Panama's," Mulino said in response to Trump's threats.

The Panama Ports Company's concession agreement was extended by 25 years in 2021.

The United States is the canal's main user, followed by China.

Since 2000, the waterway has contributed more than US$30 billion to Panama's state coffers, including nearly US$2.5 billion in the last fiscal year. (AFP)