A day after summoning the American ambassador for a formal rebuke, Iceland’s leaders on Tuesday publicly condemned a social media post from President Trump showing the American flag covering their nation along with Greenland, Canada, Mexico and Caribbean states.

“It is an insult to Icelanders, Canadians, Greenlanders,” Prime Minister Kristrun Frostadottir of Iceland told reporters on Tuesday, referring to Mr. Trump’s Monday post, which did not include any written commentary.

“There is nothing funny or normal about making fun of the sovereignty of states,” she added.

Icelanders have been wary of Mr. Trump since he threatened Greenland, their closest neighbor. Now, this social media post feels like a marked escalation in rhetoric, said Eirikur Bergmann, a politics professor at Bifrost University in Iceland.

“Icelanders are used to looking toward the U.S. as Iceland’s defender,” he said. “Now, our protector has become our intimidator.”

The American Embassy in Reykjavik declined to comment on Mr. Trump’s post or Iceland’s response, and the White House did not immediately respond to a request for comment.

Mr. Trump’s post tests Iceland’s resolve just over a week after the Nordic country voted against exploring European Union membership.

That vote sharply divided public opinion, as many of the 400,000 people living in Iceland felt like they were at a turning point. Many said that the vote came down to questions of how to protect their stability and sovereignty.

Some Icelanders, who wanted to explore membership, saw the bloc as a potential protector in a world where superpowers are circling the Arctic and Mr. Trump is shaking international alliances. Iceland, the only NATO member without its own military, relies on the alliance for protection. And Mr. Trump’s aggressive remarks about Greenland have alarmed many Icelanders.

Icelandic voters who wanted to explore E.U. talks said in interviews that they were shocked when Mr. Trump repeatedly confused Iceland with Greenland in a major speech in January. Many, too, were offended by reports that Billy Long, Mr. Trump’s pick to be the new American ambassador, joked in private that Iceland could become the 52nd state. (Mr. Long apologized.)

But late last month, those voters lost out to Icelanders who thought it would be better for Iceland to stay out of the bloc.

Now, Professor Bergmann said, Iceland’s choice to go it alone is heightening the national anxiety.

“Iceland doesn’t have the same options as before of fleeing into the arms of Brussels as a response to an intimidation like this,” he said.

In a show of sovereignty and outrage, Iceland’s government is reacting forcefully to Mr. Trump.

Thorgerdur Katrin Gunnarsdottir, the foreign minister, summoned Mr. Long to express what her ministry called a “clear message that the image was wholly inappropriate.”

The ministry did not make Ms. Gunnarsdottir available for an interview.

Ms. Gunnarsdottir told reporters that Trump administration officials had repeatedly offered her advice about their boss: “We should perhaps not take the current U.S. president literally, but we should take him seriously,” she said she was told.

This post, she said, crossed a line.

“This is not a joke in my opinion,” she said.

“And if this is supposed to be a joke,” she continued, “it’s a bad joke.”