Earlier, US President Donald Trump said he had secured total and permanent United States access to Greenland in an accord with the NATO military alliance, whose head said allies would have to step up their commitment to Arctic security to ward off threats from Russia and China.
The deal came as Trump dropped threats to impose tariffs on eight European allies for their stance on Greenland and ruled out taking the vast, mineral-rich island by force.
Stubb said he wanted a package of measures to be put together to boost Arctic security that would be "not dissimilar" to a deal agreed in The Hague last June, when NATO leaders backed a big rise in defence spending as sought by Trump.
"In an ideal world, we would have something ready by the NATO summit in Ankara," Stubb told Reuters on the sidelines of the World Economic Forum in Davos, Switzerland.
Stubb said that a more robust Arctic security architecture should draw on closer co-operation between NATO's five Scandinavian members - Sweden, Finland, Norway, Denmark and Iceland - plus the United States and Canada.
The armed forces of Finland itself were trained to operate in the region, he added.
"We have one million women and men who've done their military service in Arctic conditions," said Stubb, who many diplomats and political analysts regard as one of the European leaders most adept at building bridges with Trump.
Trump said the details of the agreement over Greenland were still being worked out on Thursday.
"It's really being negotiated now, the details of it. But essentially it's total access. It's - there's no end, there's no time limit," Trump told the Fox Business Network from the sidelines of the World Economic Forum.
Greenland's Prime Minister Jens-Frederik Nielsen welcomed Trump's latest comments but said he was still in the dark on many aspects.
"I don't know what there is in the agreement, or the deal, about my country," he told reporters in the capital Nuuk.
"We are ready to discuss a lot of things and we are ready to negotiate a better partnership and so on. But sovereignty is a red line," he added, when asked about reports that Trump was seeking control of areas around US military bases in Greenland as part of a wider deal.
"We cannot cross the red lines. We have to respect our territorial integrity. We have to respect international law and sovereignty."
Trump's threat last weekend to impose tariffs on European countries that opposed his ambition to acquire Greenland has rattled European capitals, and European Union leaders are meeting in Brussels on Thursday for talks on the issue.
Stubb said he was confident that the EU leaders would maintain a united front on Greenland and he underlined that it was especially important for the views of Danish Prime Minister Mette Frederiksen to be heard.
Frederiksen said on Thursday no negotiations had been held with NATO regarding the sovereignty of Greenland, a semi-autonomous territory of Denmark.
"It is still a difficult and serious situation but progress has also been made in the sense that we have now got things where they need to be. Namely that we can discuss how we promote common security in the Arctic region," Frederiksen said.
Trump has argued only the US can ensure Greenland's security in the face of what he says are Chinese and Russian ambitions in the Arctic.
Stubb, who extolled the role of NATO Secretary General Mark Rutte in finding common ground with Trump over Greenland, said he was optimistic about the future of the alliance.
"I think it's completely justified for President Trump to ask Europeans to do more about their defence, and also to pay more for the alliance and have more capability," he said.
"So the stronger NATO is, the better off we are."
