During a flurry of social media posts over the long holiday weekend, Trump posted a map showing the US sprawling across all of North America and extending to Greenland and Iceland.
The map was coloured in the red, white and blue stars and stripes of the US flag.
The Truth Social post offered no explanation but recalled Trump's earlier talk of making Canada the 51st state and his repeated musings about taking over Greenland, Denmark's self-governing territory.
"It's disturbing and, in many ways, completely inappropriate," Danish Foreign Minister Lars Løkke Rasmussen told the national broadcaster DR on Tuesday.
"It's obviously a sign that the US president still harbours some kind of maximalist vision in his own mind. We need to rein that in."
Iceland's Foreign Secretary Thorgerdur Katrín Gunnarsdóttir summoned US Ambassador Billy Long to make it clear the post was unacceptable, national broadcaster RÚV said.
The Arctic states have been on edge since Trump ramped up his rhetoric at the start of the year about US control of Greenland.
His post came on Monday as the European Union sought to reassure Greenland with the promise of a stronger partnership and hundreds of millions of euros in investment following Trump's repeated threats.
Iceland - just 290km away - became alarmed when Trump mistakenly named their country four times while speaking about his designs on Greenland.
Iceland is a NATO member, but the gaffe led its coalition government to move up a referendum, originally planned for next year, on whether the country should resume long-stalled negotiations to become a member of the EU.
Voters rejected the measure in August that was designed to strengthen ties with Europe to better insulate the country from geopolitical instability.
Thousands of Icelanders also signed a petition urging the prime minister to reject Long as ambassador after he made a crack earlier this year about Iceland becoming the 52nd US state and making him governor. Long apologised and took up his post in Reykjavik in August.
Trump has also riled Canada with talk of it becoming a US state, launching a trade war with it and recently renaming Lake Ontario "Lake America".
Over the Labor Day weekend, the global map was not the only thing on his mind. Trump also suggested renaming the state of New Mexico as "New America".
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