President Trump had a special message on Tuesday night for the “incredible people of Greenland,” whose island he has repeatedly expressed interest in acquiring — through a purchase or by force.

“We strongly support your right to determine your own future,” he said, briefly pausing during a speech to Congress to address Greenlanders directly. Then, with a confident nod, he added, “We will make you rich.”

Some members of Congress responded with a mix of applause, murmurs — and a few smiles. Greenlanders weren’t so enthused.

“It is up to us whether we become rich,” said Pele Broberg, the leader of one of Greenland’s major political parties.

Mr. Trump has been talking about acquiring Greenland, a large island in the Arctic Ocean, since his first term, but this was the first time he addressed the island’s 56,000 residents so directly and prominently.

“It’s a very small population but very, very large piece of land and very, very important for military security,” he told lawmakers.

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