The US secretary of state, Marco Rubio, says he plans to meet Danish officials next week to discuss Greenland, amid an escalating crisis within Nato over Donald Trump’s threats to take over the Arctic territory.

An urgent meeting had been requested by the foreign ministers of Greenland and Denmark, which has said that any invasion or seizure of the territory by its Nato ally would mark the end of the western military alliance and “post-second world war security”.

Rubio, asked whether he would rule out military intervention in Greenland, told reporters in Washington: “If the president identifies a threat to the national security of the United States, every president retains the option to address it through military means.

“As a diplomat, which is what I am now, and what we work on, we always prefer to settle it in different ways. That included in Venezuela.”

He added: “I’m not here to talk about Denmark or military intervention. I’m going to meet them next week.”

France said on Tuesday that it was working with allies on how to react if the US were to invade Greenland. The French foreign minister, Jean-Noël Barrot, said the subject would be discussed at a meeting with the German and Polish foreign ministers on Wednesday. “We want to take action, but we want to do so together with our European partners,” he told France Inter radio.

Trump claimed on Wednesday that the US would not desert Nato in a backhanded social media post that also criticised the alliance.

“We will always be there for Nato, even if they won’t be there for us,” he wrote on Truth Social. Russia and China would “have zero fear” of Nato without the US, he said. Addressing “all of those big Nato fans”, he added: “They were at 2% GDP, and most weren’t paying their bills, UNTIL I CAME ALONG.”

After one of Trump’s leading aides said on Tuesday that the US may be willing to seize control of the Arctic territory by force, European leaders rallied around Denmark and Greenland with a rare rebuke to the White House, declaring that Greenland “belongs to its people”.

Despite this, on Tuesday night, the White House said that Trump and his team were looking at “a range of options” to acquire Greenland, including using the US military, which it said was “always an option”.

But Barrot said that in a phone call on Tuesday, Rubio, had told him that he had “ruled out the possibility of an invasion” of Greenland. “I myself was on the phone yesterday with US secretary of state, Marco Rubio … who confirmed that this was not the approach taken,” he said.

Trump has long-expressed an interest in acquiring Greenland. But in recent days, after the US military operation in Venezuela on Saturday in which troops removed the country’s president, Nicolás Maduro, the Trump administration’s rhetoric – and, subsequently, international tensions – have ramped up to new heights, putting the survival of Nato into question.

On Tuesday night, the Danish parliament held an extraordinary meeting to discuss the unprecedented situation.

Lars Løkke Rasmussen, the Danish foreign minister, and his Greenlandic counterpart, Vivian Motzfeldt, said they were seeking an urgent meeting with Rubio to discuss Greenland. “We would like to add some nuance to the conversation,” Rasmussen said on social media. “The shouting match must be replaced by a more sensible dialogue. Now.”

Trump has claimed that Greenland is “full of Chinese and Russian ships” and that Denmark is incapable of defending Greenland, which the president has said is vital for US national security.

But Rasmussen said after the extraordinary meeting that the US was giving a false representation of what was happening in Greenland.

“The image that is being painted of Russian and Chinese ships right inside the Nuuk fjord and massive Chinese investments being made is not correct,” he said.

The situation, Rasmussen said, was “based on a misreading of what is up and what is down”, adding: “We are looking after the kingdom.”

Denmark’s defence minister, Troels Lund Poulsen, disputed US claims that the country was not doing enough to protect Greenland. “We have invested close to 100bn [Danish kroner] (£11.6bn) in security capabilities,” he said.