It would be “insane” for Russia to invade Ukraine — but that scenario is “not impossible,” says former Prime Minister of Sweden Carl Bildt.

“A big invasion might not be the most likely, but it’s not impossible” given that Russian President Vladimir Putin has used military power against Ukraine in the past, said Bildt, who is now co-chair of the European Council on Foreign Relations.

“It’d be insane,” he told CNBC’s “Capital Connection” on Thursday, pointing out that there will be media broadcasts of explosions and images of refugees fleeing in the event of an invasion.

The effect on Russia’s economy and society would be very substantial, and people would likely mobilize resources to help Ukraine, he predicted.

“We would be entering into really uncharted territory in terms of war and peace in Europe and security,” Bildt said.

“One would hope that the reality of what might happen is starting to sink in, into the decision-making circles, small as they are, in the Kremlin,” he added.

There are rising fears of war between Russia and Ukraine as Moscow has boosted its military presence at the border between the two countries in recent months. Talks with the U.S. and other Western powers have not yielded much progress, and Washington has called for a diplomatic path forward.

The Kremlin has denied it is planning to invade Ukraine, in a repeat of its illegal annexation and occupation of Crimea in 2014.

The impasse has put Russian assets under pressure. As of Thursday, the MOEX Russia Index had declined more than 11% since the start of the year.

Nord Stream 2 — a contentious pipeline that can carry 55 billion cubic meters of natural gas to Europe every year — has often been raised as a possible piece of leverage against Russia.

But the former Swedish prime minister isn’t hopeful.

He told CNBC he doesn’t think the project can be used in negotiations because it is likely to be operational only in the later part of 2022.

“I don’t think it’s usable as a bargaining chip,” he said, adding he’s more worried about Nord Stream 1, which has the same transportation capacity.

If Nord Stream 1 is cut, Germany will be in a critical situation, he said.

Europe relies on Russia for around 43% of its gas imports, according to Eurostat.

Bildt said there are two scenarios in which Europe’s gas supplies will be threatened.

The first is if there’s fighting and an invasion into Ukraine. “It’d be fairly difficult to see that — while the tanks are rolling and shooting on the ground — that the pipes will deliver gas just meters below them,” he said.

Gas flow may also be cut if Russia wants to retaliate against heavy Western sanctions. “The only forceful, really dangerous thing that they can do is to cut the gas supply then,” he said.

That would have a detrimental effect on Europe, and discussions are still ongoing about how to handle that possibility, he added.

The Biden administration this week said it is exploring ways to secure energy for allies in Europe if Russia reduces its oil and gas exports.

A senior administration official pointed out, however, that the Russian economy is in need of revenue “at least as much as Europe needs its energy supply.”

“This is not an asymmetric advantage for Putin. It’s an interdependency,” the official said.

— CNBC’s Amanda Macias and Silvia Amaro contributed to this report.