Turkey agreed Tuesday to lift its opposition to Sweden and Finland joining NATO, ending an impasse that had clouded a leaders' summit opening in Madrid amid Europe's worst security crisis in decades, triggered by the war in Ukraine.

After urgent top-level talks with leaders of the three countries, alliance Secretary General Jens Stoltenberg said that "we now have an agreement that paves the way for Finland and Sweden to join NATO." He called it "a historic decision."

Among its many shattering consequences, President Vladimir Putin's invasion of Ukraine has prompted Sweden and Finland to abandon their long-held nonaligned status and apply to join NATO as protection against an increasingly aggressive and unpredictable Russia — which shares a long border with Finland. Under NATO treaties, an attack on any member would be considered an attack against all and trigger a military response by the entire alliance.

NATO operates by consensus, and Turkish President Recep Tayyip Erdogan had threatened to block the Nordic pair, insisting they change their stance on Kurdish rebel groups that Turkey considers terrorists.

After weeks of diplomacy and hours of talks on Tuesday, Finnish President Sauli Niinistö said the three leaders had signed a joint agreement to break the logjam.

Turkey said it had "got what it wanted" including "full cooperation ... in the fight against" the rebel groups.

Stoltenberg said leaders of the 30-nation alliance will issue a formal invitation to the two countries to join on Wednesday. The decision has to be ratified by all individual nations, but he said he was "absolutely confident" Finland and Sweden would become members, something that could happen within months....