US President-elect Donald Trump has threatened "very high" tariffs on Denmark if it resists his effort to take control of Greenland, an autonomous Danish territory.

Asked during a news conference Tuesday if he would rule out using military or economic force in order to take control of the strategically-important island, he said: "No, I can't assure you on either of those two."

"I can say this, we need them for economic security," he said.

Trump also said he would use "economic force" against Canada and called the US-Canada border an "artificially drawn line".

Trump's remarks came as his son, Donald Trump Jr, visited Greenland.

Before arriving in the capital Nuuk, Trump Jr said he was going on a "personal day trip" to talk to people, and had no meetings planned with government officials.

When asked about Trump Jr's visit to Greenland, Danish Prime Minister Mette Frederiksen told Danish TV that "Greenland belongs to the Greenlanders" and that only the local population could determine their future.

She agreed that "Greenland is not for sale", but stressed Denmark needed very close co-operation with the US, a Nato ally.

Greenland lies on the shortest route from North America to Europe and is home to a large American space facility. It also has some of the largest deposits of rare earth minerals, which are crucial in the manufacture of batteries and high-tech devices.

Since winning re-election Trump has repeatedly returned to the idea of US territorial expansion - including taking back the Panama Canal.

During the news conference Trump said the canal "is vital to our country" and claimed "it's being operated by China". He previously accused Panama of overcharging US ships to use the waterway, which connects the Atlantic and Pacific oceans.

Panamanian President José Raúl Mulino has rejected Trump's claims and said there is "absolutely no Chinese interference" in the canal.

A Hong Kong-based company, CK Hutchison Holdings, manages two ports at the canal's entrances. The canal was built in the early 1900s and the US maintained control over the canal zone until 1977, when treaties gradually ceded the land back to Panama.

"Giving the Panama Canal to Panama was a very big mistake," Trump said.

It's unclear how serious the president-elect is about adding to the territory of the US, particularly when it comes to Canada, a country of 41 million people and the second-largest nation by area in the world.

During the news conference Trump said the US spends billions of dollars protecting Canada, and criticised imports of Canadian cars, lumber and dairy products.