Trump ramps up threats to gain control of Greenland and Panama Canal
His remarks came as his son, Donald Trump Jr, visited Greenland.
Before arriving by private jet 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 its future.
She said "Greenland is not for sale", but stressed Denmark needed close co-operation with the US, a Nato ally.
Greenland - which has a population of just 57,000 - is the world's largest island and is a strategically important part of the Arctic region.
It has wide-ranging autonomy, but its economy is largely dependent on subsidies from Copenhagen and it remains part of the kingdom of Denmark.
Greenland is also home to a large American space facility and has some of the largest deposits of rare earth minerals, which are crucial in the manufacture of batteries and high-tech devices.
Trump suggested the island is crucial to military efforts to track Chinese and Russian ships, which he said are "all over the place".
"I'm talking about protecting the free world," he told reporters.
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 negotiated under President Jimmy Carter gradually ceded the land back to Panama.
"Giving the Panama Canal to Panama was a very big mistake," Trump said. "Look, [Carter] was a good man... But that was a big mistake."
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 also repeated a number of falsehoods and odd conspiracy theories, including suggesting that Hezbollah, the Islamist militant group, was involved in the US Capitol riot of 2021.
Cover photo: Donald Trump Jr said his visit to Greenland was a "personal day trip"