BRUSSELS — The 30 NATO allies signed off on the accession protocols for Sweden and Finland on Tuesday, sending the membership bids of the two nations to the alliance capitals for legislative approvals — and possible political trouble in Turkey.

The move further increases Russia’s strategic isolation in the wake of its invasion of neighboring Ukraine in February and military struggles there since.

“This is truly a historic moment for Finland, for Sweden and for NATO,” said alliance Secretary General Jens Stoltenberg.

The 30 ambassadors and permanent representatives formally approved the decisions of last week’s NATO summit when the alliance made the historic decision to invite Russia’s neighbor Finland and Scandinavian partner Sweden to join the military club.

Parliamentary approval in member state Turkey could still pose problems for their final inclusion as members, despite a memorandum of understanding reached between the three.

Last week, Turkey’s leader, Recep Tayyip Erdogan, warned that Ankara could still block the process if the two countries fail to fully meet Turkey’s demand to extradite terror suspects with links to outlawed Kurdish groups or the network of an exiled cleric accused of a failed 2016 coup in Turkey.

He said Turkey’s Parliament could refuse to ratify the deal. It is a potent threat since NATO accession must be formally approved by all 30 member states, which gives each a blocking right.

Mr. Stoltenberg said he expected no change of heart. “There were security concerns that needed to be addressed. And we did what we always do at NATO. We found common ground.”

At a news conference, the foreign ministers of Sweden and Finland were peppered with questions about whether a specific list of people would need to be extradited to Turkey, but both said such a list was not part of the memorandum with Ankara.

“We will honor that memorandum and follow up on that,” said Sweden’s foreign minister, Ann Linde, adding her government’s actions would always “comply with the Swedish legislation. We will comply with international law.”

She added, though, that “we will see to it that we have a mechanism of fighting terrorism in all its forms.”

Every alliance nation has different legislative challenges and procedures to deal with, and it could take several more months for the two to become official members.

Germany’s parliament is set to ratify the membership bids on Friday, according to coalition party Free Democrats. Other parliaments might only get to the approval process after the long summer break.

“I look forward to a swift ratification process,” said the Finnish foreign minister, Pekka Haavisto. The Russian invasion of Ukraine has given the process added urgency. It will ensconce the two nations in the Western military alliance and give NATO more clout, especially in the face of Moscow’s military threat.

“We will be even stronger and our people will be even safer as we face the biggest security crisis in decades,” said Mr. Stoltenberg.

Tuesday’s signing-off does bring both nations deeper into NATO’s fold already. As close partners, they already attended some meetings that involved issues that immediately affected them. As official invitees, they can attend all meetings of the ambassadors even if they do not yet have any voting rights.