President Donald Trump and his team are considering "a range of options" in order to acquire Greenland — including "utilizing the U.S. Military," White House press secretary Karoline Leavitt told CNBC on Tuesday.

The statement further escalates the Trump administration's already aggressive rhetoric about Greenland, which the president has long sought to make a part of the United States.

Trump said Sunday that the U.S. needs the Arctic island for national security purposes, pointing to Russian and Chinese activities in the region.

Greenland is a territory of Denmark, which, like the U.S., is a member of the NATO international military alliance.

The leaders of Denmark and other European NATO states on Tuesday morning issued a joint statement pushing back on Trump's increasingly vocal desire to obtain Greenland.

"Greenland belongs to its people. It is for Denmark and Greenland, and them only, to decide on matters concerning Denmark and Greenland," their statement said.

Leavitt's new comment on Greenland came after that joint statement was issued.

"President Trump has made it well known that acquiring Greenland is a national security priority of the United States, and it's vital to deter our adversaries in the Arctic region," Leavitt said in an emailed statement.

"The President and his team are discussing a range of options to pursue this important foreign policy goal, and of course, utilizing the U.S. Military is always an option at the Commander in Chief's disposal," she said.

Secretary of State Marco Rubio, however, told lawmakers during a closed briefing Monday that the administration's goal is to buy Greenland from Denmark, the Wall Street Journal reported Tuesday afternoon.

Trump has spoken frequently about absorbing both Greenland and Canada into the U.S., as well as the Panama Canal. The controversial comments have drawn international rebukes, though they were dismissed by some as unserious and unlikely to materialize in U.S. foreign policy.

The president's renewed discussion of Greenland has prompted more serious concerns in recent days, after the U.S. military entered Venezuela and successfully captured that country's leader, Nicolás Maduro, and his wife, Cilia Flores.

Trump said after that operation that "we are going to run the country until such time as we can do a safe, proper and judicious transition."

Trump also said that U.S. oil companies will enter Venezuela and "fix" the country's energy infrastructure, and that those firms "will be reimbursed" for their efforts.

Trump told The Atlantic on Sunday morning that he will leave it up to others to decide what the intervention in Venezuela means for Greenland.

"He has lost his damn mind," said Rep. Jim McGovern, D-Mass., when asked by CNBC about Trump's Greenland threats.

"I think you have to take him seriously, because he does outrageous things," McGovern added.

White House senior advisor Stephen Miller said Monday in a CNN interview that the U.S. "should have Greenland as part of the United States."

Miller also refused to rule out taking control of the island by force, but asserted that such questions are moot. "Nobody's going to fight the United States militarily over the future of Greenland," he said.

But Sen. Chris Murphy, D-Conn., told reporters on Capitol Hill on Tuesday that NATO countries would "of course" have to defend Greenland against the U.S. if necessary.

"That's what Article 5 says. Article 5 did not anticipate that the invading country would be a member of NATO," Murphy said. "We're laughing, but this is not actually something to laugh about now because I think he's increasingly serious."

On Tuesday, Sen. Ruben Gallego, D-Ariz., announced he would introduce a resolution in Congress to block Trump from invading Greenland.

"WAKE UP. Trump is telling us exactly what he wants to do," Gallego said in an X post. "We must stop him before he invades another country on a whim."

— CNBC's Justin Papp contributed to this report.