Iceland has summoned the US ambassador after President Donald Trump posted a map on social media that appeared to show Iceland and several other countries covered by the American flag.

Trump posted the image on Truth Social on Monday, showing the US, Canada, Greenland, Iceland, Mexico, Central America and the Caribbean covered in stars and stripes. The entire landmass was labelled "United States of America".

Iceland's foreign minister said the post was "completely inappropriate".

Trump's territorial ambitions have repeatedly strained relations with neighbouring countries, including his push to acquire Greenland and calls to make Canada America's 51st state.

His post of the map did not include a caption and preceded a flurry of map posts renaming the US state of New Mexico as "New America".

Responding to Trump's post, Iceland's Foreign Minister Þorgerður Katrín Gunnarsdóttir called in US ambassador to Iceland Billy Long, who formally took up the post last month, local media reported.

When an ambassador is summoned, it typically means they are being called for a formal meeting, where the host country will express displeasure over their government's actions.

The post also drew criticism from Danish Prime Minister Mette Frederiksen, who said on Monday that the position of Greenland's government and people had been made clear.

"The Greenlandic government and the Greenlandic people have said again and again that they do not want to be American," she told Danish news agency Ritzau in Nuuk.

"I hope no one is in any doubt about that, either in the United States or the rest of the world."

Trump's interest in Greenland has been a recurring theme on his social media accounts and in speeches since he took office again last year, claiming the island is necessary to the US to shore up its national security.

His post came shortly after the European Commission announced a €200m (£172m) investment in the Danish territory during a visit by Commission president Ursula von der Leyen and Frederiksen.

The European Commission said its investment would focus on education, internet connectivity, the use of raw materials in the country and hydropower energy.

Meanwhile, Mexican President Claudia Sheinbaum said Mexico "is neither nor will be a colony or protectorate of any foreign country," after Trump's post.

"Proudly we are a free, independent, and sovereign nation," she wrote on social media.