Although there is little doubt that the Senate and most other NATO members will overwhelmingly approve an accession treaty, Turkey – which under President Recep Tayyip Erdogan has had a sometimes close and sometimes controversial relationship with Moscow – has expressed objections that could slow down process and requires negotiation to solve its problems.

“These two countries, especially Sweden, they are a complete hotbed of terrorism,” Erdogan said on Thursday, a clear reference to what the Turkish leader claims is their silent support for Kurdish separatists.

Foreign Minister Antony J. Blinken met with his Turkish counterpart in New York on Wednesday, and Finnish officials said they were also in talks with Turkey. In a conversation with reporters on Wednesday, Jake Sullivan, Mr Biden’s national security adviser, expressed confidence that “Turkey’s concerns can be resolved” and that Finland and Sweden could eventually join the alliance.

But Mr Erdogan is famously unpredictable, and he could easily take advantage of his leverage as a potential spoiler to push his own demands, including lifting sanctions against his country for its purchase of Russian-made air defense systems.

Jens Stoltenberg, NATO Secretary General, said on Thursday that he expects to resolve Turkey’s concerns.

“I am convinced that we will make a quick decision to welcome both Sweden and Finland to join the NATO family,” he said, adding, “We address the concerns expressed by Turkey.”

Aside from Mr Erdogan’s demands, the White House ceremony was a remarkable moment in the history of the Western Alliance – a rare case in history where a single event, Russia’s invasion, changed sentiment, and probably NATO’s borders, almost overnight.

Under an agreement with the Soviet Union, Finland stayed out of the alliance, which was created to hold back Russia after World War II. It remained independent during the post-Soviet era even after joining the European Union and growing ever closer to the Western world. Until now, Sweden had adhered to more than 200 years of neutrality.

But that attitude has been quickly abandoned after Putin’s decision in February to invade Ukraine, which is not a member of NATO. Both Finland and Sweden suddenly realized that the threat from Russia had changed and that their status as spectators to major power conflicts was now a huge risk.

The speed of the turnaround has been so great that there has been virtually no debate since the fall of the Berlin Wall in 1989, when even some of Washington’s most experienced Cold War diplomats warned that the more Russia felt encircled, the higher the chances of it may eventually turn out, especially if efforts to integrate the country with the West failed.

On Wednesday, Mr. Sullivan that Mr. Biden had asked his national security officials if they supported the addition of Finland and Sweden to the alliance and that they had “emphatically supported” the move in a unanimous manner.

The Rose Garden ceremony deliberately echoed a state visit, complete with a military band. Mr Biden characterized the transition to Finland and Sweden in the alliance as almost a formality, noting that both countries had contributed forces to conflicts in Kosovo, Afghanistan and Iraq – the most important NATO commitments over the past 20 years – and that they were strong. democracies that “meet all NATO requirements and more.”

Mr Biden claimed that the two countries would increase the alliance’s firepower.

Finland has a sophisticated military that conducts complex operations to track Russian activity in the seas of northern Europe and spends heavily on modern equipment. Sweden is a more difficult case: it dismantled part of its military power and would, as Andersson admitted, need to reorient its budget to spend 2 percent of its gross domestic product on defense, the goal for NATO members.

But for the United States, the primary benefit of the Nordic countries joining the alliance is the message sent to Putin. In December, the Russian president demanded that the United States and NATO sign a treaty withdrawing forces from former Soviet states and restricting training activities and the deployment of weapons.

Instead, NATO’s border with Russia would now stretch another 810 miles, and the alliance’s expanded capabilities would complicate Russia’s defense.

Mr Putin’s expected response is the subject of speculation and planning sessions. The Russian leader and his aides have so far responded calmly, calling the move a mistake and saying they would react if weapons were placed near Russia’s borders.

But Finland and Sweden now see Mr Putin as a much greater threat to their security than Soviet leaders were during the Cold War. For Mr. Biden is the change in sentiment in the two countries an opportunity to fundamentally strengthen the transatlantic alliance and weaken Russia while Putin remains in power.

Mr Biden alluded to that goal – which he has not fully formulated – in his comments at the White House on Thursday. “In recent years, doubts have begun to arise,” he said. “Was NATO still relevant?”

He said that the Russian invasion proved that it remained “the indispensable alliance of the world we face today” and that the decisions taken by Sweden and Finland to choose sides were “proof of this commitment.”

“Finland and Sweden make NATO stronger,” he said, “not just because of their capabilities but because they are strong, strong democracies.”

Prior to the visit by Niinisto and Ms Andersson, Biden also issued a statement offering an informal security guarantee to the two nations while they await formal membership in the alliance. It was intended to prevent any attempt by Russia to intimidate the countries – perhaps with cyber attacks, perhaps with air or naval exercises – while they wait for membership, and the formal protections that come with it.

But Mr Niinisto alluded to the importance of speed. “Now that we have taken this first decisive step, it is time for NATO’s allies to weigh in,” he said. “We hope for strong support from all allies and for a rapid ratification of our membership once it has been agreed.”

He referred directly to Turkey, saying that “we will commit ourselves to Turkey’s security, just as Turkey will commit itself to our security,” adding, “We take terrorism seriously.” It seemed to be an allusion to the Turks’ concerns for the Kurdish militants.

Ms Andersson, who turned to Mr Biden and noted with laughter that “Swedes first set foot in your home state of Delaware in 1638”, said the invasion of Ukraine “reminds us of the darkest days in European history.” It was “a watershed for Sweden”, she said, which forced Swedes to rethink the core of their security.