US President-elect Donald Trump has ramped up threats to seize control of Greenland and the Panama Canal, calling both critical to US national security.

Asked on Tuesday if he would rule out using military or economic force in order to take over the autonomous Danish territory or the Canal, he responded: “No, I can’t assure you on either of those two.

“But I can say this, we need them for economic security,” he told reporters during a sprawling news conference at his Mar-a-Lago estate in Florida.

Both Denmark and Panama have rejected any suggestion that they would give up territory.

Trump also vowed to use “economic force” when asked if he would attempt to annex Canada and called the US-Canada border an “artificially drawn line”.

The news conference was initially billed as an economic development announcement to unveil Dubai developer Damac Properties’ $20 billion investment to build data centres in the US.

But the president-elect went on to criticise environmental regulations, the US election system, the various legal cases against him and President Joe Biden. Among a wide variety of other things, he suggested renaming the Gulf of Mexico the “Gulf of America” and said windmills are “driving the whales crazy”.

His remarks came as his son, Donald Trump Jr, was visiting 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 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 called the US-Canada border an “artificially drawn line” and said the US spends billions of dollars protecting Canada, and criticised imports of Canadian cars, lumber and dairy products.

“They should be a state,” he told reporters.

During the news conference, Trump also repeated a number of falsehoods and odd conspiracy theories, including suggesting that the FBI was a key driver of the Capitol riot on 6 January 2021, and suggesting that Hezbollah, the Islamist militant group, was also involved.