MADRID — NATO leaders were sitting down Wednesday to try to turn an urgent sense of purpose triggered by Russia’s invasion of Ukraine into action — and to patch up any cracks in their unity over money and mission.

Secretary-General Jens Stoltenberg said the alliance was meeting in Madrid “in the midst of the most serious security crisis we have faced since the Second World War.”

Russia’s invasion of its neighbor has shattered Europe’s peace and driven NATO to pour troops and weapons into eastern Europe on a scale not seen since the Cold War.

Members of the alliance have also sent billions in military and civilian aid to Ukraine. The 30 NATO leaders will hear directly from Ukrainian President Volodymyr Zelenskyy, who is likely to ask them to do even more when he addresses the gathering by video link.

U.S. President Joe Biden, whose country provides the bulk of NATO’s military power, said Tuesday in Madrid that the alliance was “as united and galvanized as I think we have ever been.”

But NATO allies are showing signs of strain as the cost of energy and other essential goods has skyrocketed amid the war and tough Western sanctions on Russia. There also are tensions over how the war will end and what, if any, concessions Ukraine should make to stop the fighting.

Money could also be a sensitive issue — just nine of NATO’s 30 members currently meet the organization’s target of spending 2% of gross domestic product on defense.

British Prime Minister Boris Johnson, whose country does hit the target, urged NATO allies “to dig deep to restore deterrence and ensure defense in the decade ahead.”

The war has already triggered a big increase in NATO’s forces in eastern Europe, and allies are expected to agree at the summit to increase the strength of the alliance’s rapid reaction force nearly eightfold, from 40,000 to 300,000 troops by next year. The troops will be based in their home nations, but dedicated to specific countries on NATO’s eastern flank, where the alliance plans to build up stocks of equipment and ammunition.

Biden set out plans to beef up the American military presence in Europe, with more U.S. troops in the east and two more Navy destroyers based in Rota, Spain.

Stoltenberg said NATO was undertaking “the biggest overhaul of our collective defense since the end of the Cold War.”

The leaders are also set to publish NATO’s new Strategic Concep t, its once-a-decade set of priorities and goals.

The last such document, in 2010, called Russia a “strategic partner” for NATO. Now Russia is set to be declared the alliance’s number one threat. The the document will also set out NATO’s approach on issues from cybersecurity to climate change — and the growing economic and military reach of China.

For the first time, the leaders of Japan, Australia, South Korea and New Zealand are attending the summit as guests, a reflection of the growing importance of the Indo-Pacific region.

Stoltenberg said China was not NATO’s adversary, but posed “challenges to our values, to our interest and to our security.”

Biden was due to hold a rare joint meeting with Japanese Prime Minister Fumio Kishida and South Korean President Yoon Suk Yeol on the sidelines of the summit, focused on North Korea’s nuclear program.

The summit opened with one problem solved, after Turkey agreed Tuesday to lift its opposition to Sweden and Finland joining NATO. In response to the invasion, the two Nordic nations abandoned their long-held nonaligned status and applied to join NATO as protection against an increasingly aggressive and unpredictable Russia — which shares a long border with Finland.

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 urgent top-level talks with leaders of the three countries, alliance Secretary Stoltenberg said the impasse had been cleared.

Turkey hailed Tuesday’s agreement as a triumph, saying the Nordic nations had agreed to crack down on groups that Ankara deems national security threats, including the Kurdistan Workers’ Party, or PKK, and its Syrian extension. It said they also agreed “not to impose embargo restrictions in the field of defense industry” on Turkey and to take “concrete steps on the extradition of terrorist criminals.”

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

Stoltenberg said he expected the process to be finished “rather quickly,” but did not set a time on it.