Mette Frederiksen has said that Denmark is at a “fateful moment” amid Donald Trump’s threats to take over Greenland, accusing the US of potentially turning its back on Nato.

Speaking at a party leader debate at a political rally on Sunday, the Danish prime minister said her country was “at a crossroads”.

Her comments came before a crucial week in increasingly tense relations between Denmark, Greenland and the US in which the foreign ministers of Denmark and Greenland, Lars Løkke Rasmussen and Vivian Motzfeldt, are due to meet the US secretary of state, Marco Rubio.

“We are at a crossroads, and this is a fateful moment,” said Frederiksen. “What is at stake is bigger than what the eye can see, because if what we experience from the Americans is that they are actually turning their backs on the western alliance, that they are turning their backs on our Nato cooperation by threatening an ally, which we have not experienced before, then everything will stop.”

On Friday, Trump said the US would take action on Greenland “whether they like it or not”. He said: “We’re going to be doing something with Greenland, either the nice way or the more difficult way.” His administration has refused repeatedly to rule out the use of military force – despite Denmark and Greenland being Nato allies.

The Greenlandic prime minister, Jens-Frederik Nielsen, alongside the leaders of the country’s four other political parties, responded by issuing a united statement that read: “We don’t want to be Americans, we don’t want to be Danish, we want to be Greenlanders. The future of Greenland must be decided by Greenlanders.”

At the domestic political debate in Nyborg, Frederiksen said although she had seen Trump since then, she had not discussed Greenland with him since a phone call a year ago. Denmark was, she said, “doing everything we can to make our position prevail in an American reality” but that it had to “stand firm” on the issue of Greenland.

She said: “In our time, there will be a lot of setbacks where you can only choose between what is right and wrong, and this is one of them.”

Describing the current situation between the longtime allies as a “conflict over Greenland”, she said: “We have received massive support from the countries in Nato.”

Meanwhile, at a national conference of people and defence in Sälen, north-west Sweden, the Swedish prime minister, Ulf Kristersson, spoke out in support of neighbouring Denmark.

The US, he said, should thank Denmark for its longtime loyalty rather than issuing “threatening rhetoric” against Denmark and Greenland.

He also condemned the US attack on Venezuela, saying it violated international law and “risks encouraging more countries to act similarly”.

Sweden on Sunday announced that it was to invest about 15bn Swedish kronor (£1.21bn) in territorial air defence capabilities.

“The world we know continues to be shaken,” said Kristersson. “Take it seriously, but don’t panic. We shouldn’t be afraid, but we should be prepared.”