GEOFF BENNETT: Today, president-elect Trump's allies in Congress proposed a new bill dubbed Make Greenland Great Again.

It's meant to expedite a negotiation process with Denmark, which protects Greenland's autonomy, given Mr. Trump's repeated desire to buy the Arctic territory.

Meantime, Greenland's prime minister said today that while the massive island is not for sale, Greenland would work with the U.S. Nick Schifrin has this look at the isolated, but strategic polar outpost.

NICK SCHIFRIN: It is the world's largest island, majestic, magical, remote and rugged, an ancient part of the planet crucial for contemporary national security.

SHERRI GOODMAN, International Military Council on Climate and Security: It is a key part of the Arctic region that protects access to the U.S. homeland.

NICK SCHIFRIN: Sherri Goodman is the secretary-general of the International Military Council on Climate and Security and a senior fellow at the Woodrow Wilson Center.

SHERRI GOODMAN: It has long been a place where we have defended against Soviet missiles during the Cold War through a large base in the northwest of Greenland, now upgraded to a space base today.

At Greenland, we are able to defend against Russian or Chinese incoming attacks.

NICK SCHIFRIN: Greenland sits in the middle of the shortest route between the U.S. and Europe and hosts the U.S.' northernmost base, now called the Pituffik Space Base, home to a ballistic missile early warning system.

It's also home to untapped riches beneath the ice, oil and gas, iron ore and gold and rare earths, whose promise is creating a race among the great powers.

SHERRI GOODMAN: China has increasingly been seeking investment in Greenland and in other parts of the Arctic.

And I think the U.S. is eying minerals for batteries, for advanced technologies, and to power the clean energy economy.

DONALD TRUMP, Former President of the United States (R) and Current U.S. President-Elect: We need it for national security.

That's for the free world.

I'm talking about protecting the free world.

NICK SCHIFRIN: Last week, president-elect Trump pitched buying Greenland to protect against Russia and China.

DONALD TRUMP: You don't even need binoculars.

You look outside, you have China ships all over the place.

You have Russian ships all over the place.

We're not letting that happen.

NICK SCHIFRIN: Greenland's been part of the kingdom of Denmark since 1721.

Today, it's a self-governing territory that gained autonomy in 1979.

And while Greenland and Denmark said they're not open for purchase, they might be open for business.

METTE FREDERIKSEN, Prime Minister of Denmark (through translator): The United States is our closest ally, and from our side we will do everything we can to continue to have close cooperation.

NICK SCHIFRIN: But Trump also refused to rule out trying to seize Greenland with the U.S. military.

DONALD TRUMP: I'm not going to commit to that now.

It might be that you will have to do something.

NICK SCHIFRIN: And that led to European warnings, even comparing Trump's threat to Russia's full-scale invasion of Ukraine.

JEAN-NOEL BARROT, French Europe and Foreign Affairs Minister (through translator): You are asking me if I think the United States will invade Greenland.

The answer is no.

Have we entered an era that sees the return of the survival of the fittest?

The answer is yes.

It is out of the question for the European Union to let any nation in the world, whichever it is, and let me say starting with Russia, to attack its sovereign borders.

SHERRI GOODMAN: Putin would like nothing better than to continue to drive a wedge between the United States and its NATO allies.

So, in that sense, I think this type of discussion is very unhelpful.

We're not going to be using military force to take over Greenland.

We're using military force to defend against Russian and Chinese actions in and around Greenland.

NICK SCHIFRIN: But this isn't the first time Trump has expressed interest.

DONALD TRUMP: Essentially, it's a large real estate deal.

And strategically for the United States, it would be nice.

NICK SCHIFRIN: And Trump wasn't the first American president who thought that.

In the 1860s, the Andrew Johnson administration bought Canada and considered buying Greenland.

The Truman administration secretly offered Denmark $100 million in gold or to swap parts of Alaska.

But the island's national security importance has accelerated as its ice melts, thanks to climate change.

DAVID HOLLAND, New York University: Land is very valuable since they stopped making it.

And so the idea that new land can appear is an enormous resource to anyone.

NICK SCHIFRIN: David Holland is a New York University professor of environmental sciences.

He's visited Greenland 30 times and has dedicated his life to decoding the Arctic and its long-term impact on the planet.

DAVID HOLLAND: Greenland is perhaps now likely to melt significantly, if not completely, and to become an island without ice.

And you scale it 1,000 years, that is a lot of change in sea level, a lot of change in the global coastline.

NICK SCHIFRIN: And possible change to the climate that could be so accelerated and dramatic, it inspires Hollywood dystopias.

DAVID HOLLAND: When you remove a mountain, because Greenland is a mountain, more than a mile high of ice sitting north of the U.S., and so weather patterns will be changed by the removal of that mountain range.

"The Day After Tomorrow" is really a story about Greenland and the ocean adjacent to it and how critical and special that place on Earth is to our climate.

NICK SCHIFRIN: Greenland is so large, it serves as a kind of thermostat that keeps the climate balanced.

If it melts, the thermostat could break.

DAVID HOLLAND: If you abstract and look at Earth from space, you see Earth as a blue and white sphere or marble, and the white reflects all the sunlight from the sun back to space and the blue parts absorb a lot of heat.

We are in danger of losing the ice and changing the color of the Earth, such that it becomes effectively more blue or green and absorbing a lot more heat.

And that change is far bigger by many times over than the change to the greenhouse gases.

NICK SCHIFRIN: All of that might not be at the top of the new administration's mind.

Trump has dismissed manmade climate change as a hoax.

But the ice is melting, and that makes this enchanted land ever more crucial and coveted.

For the "PBS News Hour," I'm Nick Schifrin.