Donald Trump’s special envoy to Greenland said a deal for Washington to take over the island “should and will be made” as a US congressional delegation visited Copenhagen in a show of support.

Jeff Landry said he planned to visit Greenland in March and that the US president “is serious” about acquiring the largely autonomous territory, which is part of the Danish kingdom.

His comments came as a bipartisan group of 11 members of the House and Senate – including the Republican senators Thom Tillis and Lisa Murkowski and the Democrat senator Chris Coons – travelled to the capital of Denmark to meet the Danish and Greenlandic leaders, Mette Frederiksen and Jens-Frederik Nielsen, in a show of solidarity against Trump’s threats of military intervention.

“I do believe that there’s a deal that should and will be made once this plays out,” Landry told Fox News on Friday.

He added: “The president is serious. I think he’s laid the markers down.

“He’s told Denmark what he’s looking for, and now it’s a matter of having Secretary Rubio and Vice-President JD Vance make a deal.”

Denmark announced it had agreed to provide support to help Greenland’s emergency preparedness.

Torsten Schack Pedersen, Denmark’s minister for public safety and emergency preparedness, said: “It is important that we stand together.”

Peter Borg, Greenland’s minister for fisheries, hunting, agriculture, self-sufficiency and environment, said his government “appreciates the support from Denmark to strengthen preparedness in Greenland”.

This week, Greenlanders living in the capital, Nuuk, said they were so afraid of the threat from the US that they were watching the skies and seas themselves. In the absence of emergency preparedness support from authorities, many said they had been left to work out their own plans on what to do in the case of emergency evacuation or capture by US forces.

During the congressional visit to Denmark, for which the Greenlandic flag, Erfalasorput, was flown at Christiansborg Palace, the US lawmakers were due to meet other Danish and Greenlandic politicians as well as Frederiksen and Nielsen.

Arriving at a lunch meeting at the Confederation of Danish Industry, the Democrat Steny Hoyer told TV 2: “Keep the faith. You’ve got a lot of people with you.”

After Wednesday’s closely watched high-stakes meeting between the US secretary of state, Marco Rubio, the US vice-president, Vance, and the foreign ministers of Greenland and Denmark, the two sides gave starkly contrasting accounts of what was agreed.

The White House press secretary, Karoline Leavitt, on Thursday claimed that a delegation from Denmark and Greenland had agreed to “continue to have technical talks on the acquisition of Greenland”.

But Lars Løkke Rasmussen and Vivian Motzfeldt, the foreign ministers of Denmark and Greenland respectively, contradicted her claims.

Løkke said they had not made such an agreement, but had formed a working group to investigate whether it was possible to “accommodate” US security wishes for the Arctic region.

Motzfeldt said Leavitt had not been at the meeting, telling the Greenland newspaper Sermitsiaq: “There is a lot of work ahead, the situation is still very uncertain, but we have a new channel, a place where we can talk directly to each other.”

On Thursday, Frederiksen said Greenland’s defence was a “common concern” for Nato as international troops started arriving in Greenland from across Europe.

A spokesperson for the German defence ministry said on Friday that the reconnaissance mission would assess the viability of deploying Eurofighter jets to the territory.

“It is a matter of looking at whether the Arctic is secure and to what extent we can contribute to this together with our Nato partners,” the spokesperson said.