Washington — The U.S. and Denmark still have "fundamental" differences over the future of Greenland, but will continue to talk, Denmark's foreign minister said after a White House meeting Wednesday amid President Trump's push to take over the Arctic island.

Denmark's foreign minister, Lars Loekke Rasmussen, met with Greenland's minister for foreign affairs, Vice President JD Vance, Secretary of State Marco Rubio and other officials. Loekke Rasmussen described the meeting as a "frank but also constructive discussion" on security long-term security in Greenland. 

The Danish official said they've agreed to establish a high-level working group to determine a way forward on Greenland, as Mr. Trump remains intent on acquiring the semi-autonomous territory within the Kingdom of Denmark. Loekke Rasmussen said they "still have a fundamental disagreement, but we also agree to disagree." 

"There is clearly a disagreement," he said in a press conference with reporters in Washington. "We agree that it makes sense to try to sit down on a high level to explore whether there are possibilities to accommodate the concerns of the president while we at the same time respect the red lines of the Kingdom of Denmark."

"Whether that is doable, I don't know," Loekke Rasmussen said, adding he hopes they can "take down the temperature." The Danes asked for the meeting. 

Loekke Rasmussen said he agrees that the security situation in the Arctic has changed, and said he's "eager" to work with the U.S. on security improvements. But the framework for improving Arctic security through NATO already exists, he said, and the U.S. acquiring Greenland is "absolutely not necessary."

Vivian Motzfeldt, Greenland's minister of foreign affairs, told reporters it's never been more important to strengthen their ties with the U.S., "but that doesn't mean that we want to be owned by the United States."

Asked if he would respect the red lines set forth by Greenland and Denmark, Mr. Trump told reporters in the Oval Office, "Well, we're going to see what happens with Greenland," adding that he hasn't yet been briefed on the meeting. 

"We need Greenland for national security, so we're going to see what happens," Mr. Trump said.

Asked whether he would leave NATO over the Greenland issue, the president said he wouldn't broadcast his options.

The meeting came one day after Greenland's Prime Minister Jens-Frederik Nielsen said at a news conference, "If we have to choose between the United States and Denmark here and now, we choose Denmark."

Mr. Trump has repeatedly said he wants to acquire Greenland, a semi-autonomous territory of Denmark, citing national security reasons. He repeated that again on Wednesday morning, saying "it is vital for the Golden Dome that we are building" and that "NATO should be leading the way for us to get it."

"IF WE DON'T, RUSSIA OR CHINA WILL, AND THAT IS NOT GOING TO HAPPEN!" Mr. Trump said in a post on Truth Social. 

"NATO becomes far more formidable and effective with Greenland in the hands of the UNITED STATES," he said. "Anything less than that is unacceptable."

On Tuesday, Mr. Trump told reporters that if Greenland's premier said the territory wanted to stay part of Denmark, "that's their problem."

"I disagree with him," Mr. Trump said. "I don't know who he is, don't know anything about him, but that's going to be a big problem for him." 

Leaders of both Denmark and Greenland have stated Greenland is "not for sale," which has led Trump officials to say that the administration is considering all options, including military force. 

"I'd love to make a deal with them. It's easier," Mr. Trump said Sunday. "But one way or the other, we're going to have Greenland." Rubio has downplayed the possibility of military force to acquire Greenland.

Vance visited Greenland last year. Danish Prime Minister Mette Frederiksen said Tuesday that the Trump administration is applying "completely unacceptable pressure from our closest ally." 

Frederiksen said earlier this month that an American military move to seize control of Greenland would amount to the end of the NATO military alliance. Denmark is a NATO member, and NATO's Article 5 states that if a NATO ally suffers an armed attack, all members will consider it an attack on them as well and do what they need to aid the attacked nation.

Tensions were high ahead of the meeting, as was concern about a further fracturing of the relationship with the U.S. NATO ally, sources familiar with the situation told CBS News. The Danish government expected to present an offer for enhanced cooperation with the U.S. and access in Greenland in terms of military presence and NATO presence, the sources said.

The Danes wanted clarity on what the U.S. is pressing for beyond that offer, and whether a financial plus-up is being demanded, the sources said. They wanted to know if Mr. Trump's intent is to have control or political ownership, which concerns them, given the clear objection of the Greenlandic government to either. Greenlandic officials have been clear that they want the island to belong to Denmark.

A European official from a nearby country said there is some concern that Denmark may be miscalculating by demanding this meeting with the U.S. because it could formalize and potentially harden positions around what could otherwise be rhetorical pressure by Mr. Trump.

On Wednesday, Republican Sen. Mitch McConnell of Kentucky took to the Senate floor to voice his disapproval of intervening in Greenland's affairs and to emphasize the importance of maintaining a united NATO alliance. 

"Unless and until the President can demonstrate otherwise, then the proposition at hand today is very straightforward: incinerating the hard-won trust of loyal allies in exchange for no meaningful change in U.S. access to the Arctic," McConnell said. "That's allies – plural. Because this is about more than Greenland. It's about more than America's relationship with its highly capable Nordic allies. It's about whether the United States intends to face a constellation of strategic adversaries with capable friends … or commit an unprecedented act of strategic self-harm and go it alone."