Nauseda told Reuters an interview on the sidelines of the World Economic Forum's annual meeting that the Greenland row was overshadowing the war in Ukraine and playing into Russia's hands, and urged the US to de-escalate tensions.
"The best outcome would be just to agree on common responsibility on the security of the Arctic region and North Atlantic region. Is it possible to achieve? We should do our best to go this way because this is the best way," he said.
US President Donald Trump said on Tuesday there was "no going back" on his aim of acquiring Greenland, refusing to rule out taking the Arctic island by force and rounding on allies.
Trump's ambition to wrest sovereignty over Greenland from fellow NATO member Denmark has threatened to tear apart the military alliance that has underpinned North American and European security for decades.
European Union leaders are due to discuss their options at an emergency summit on Thursday which Nauseda said would show whether the bloc can present a united front over Greenland.
He said the next two weeks would probably show how the dispute is resolved.
Nauseda said he hoped countries that can be sceptical about militarily supporting Ukraine would understand that Europe has reached a critical juncture, arguing NATO's future is at stake.
Trump is due to speak in Davos on Wednesday and Nauseda said his hope was that the US president would send out some signals towards de-escalating tensions over Greenland.
Describing upholding territorial integrity as an "untouchable principle," Nauseda said there was always room to de-escalate.
"But of course the precondition is that both sides want this de-escalation, and now I'm not sure. Europe is obviously willing to de-escalate. I hope that the United States will be too."
The Lithuanian president said the Greenland dispute had diverted attention away from Russia's invasion of Ukraine, posing additional challenges for Europe's eastern flank.
European Commission President Ursula von der Leyen pushed back against Trump's announcement that, starting on February, a 10 per cent import tax will be imposed on goods from eight European countries that have rallied around Denmark if the US is not able to purchase Greenland.
She vowed that the EU's response "will be unflinching, united and proportional".
Greenland's Prime Minister Jens-Frederik Nielsen said at a news conference in the island's capital Nuuk on Tuesday that "we need to have respect for international law and territorial integrity".
He said those principles should unite democratic countries, and said he was grateful for support from EU allies.
"International law, it's not a game," he said.
"We have been a close and loyal ally to the United States, to NATO, through many, many, many years. We can do lots more in that framework. We are willing to co-operate much more but of course in mutual respect, and if we cannot see that, it will be very difficult to have a good and reliable partnership."
Denmark has asked NATO for a permanent presence on Greenland, Danish Prime Minister Mette Frederiksen said on Tuesday.
She said the increased NATO presence in the Baltic Sea and the Baltic States could serve as a model for this.
Danish Defence Minister Troels Lund Poulsen and Greenlandic Foreign Minister Vivian Motzfeldt had requested a NATO mission for the Arctic region during a meeting with NATO Secretary General Mark Rutte on Monday.
Frederiksen said "a stronger NATO strategy was positively received" at the meeting with the military alliance head in Brussels.
Denmark is strengthening its military presence in Greenland.
Last week, soldiers from several European NATO countries were on the island for a multi-day Danish-led reconnaissance tour.
with DPA and AP
