BRUSSELS—For the second time this month, a major security crisis involving a member of the North Atlantic Treaty Organization has occurred, with the alliance kept on the sidelines.

Neither France, which was rocked by the Nov. 13 Paris attacks that left 130 people dead at the hands of Islamic State terrorists, nor Turkey, which downed a Russian plane striking at Turkmen fighters in Syria this week, invoked the NATO treaty or its collective defense provisions—raising questions about whether the alliance has a genuine role to play in countering terrorism or Middle East instability.

“It is upon Turkey to call on NATO action or it is upon France to call on NATO action,” said Bruno Lete, an analyst at the Brussels office of the German Marshall Fund of the United States. “If member states prefer to keep NATO out of the game, then this is what is happening.”

Critics inside and outside the alliance say NATO may not be the right vehicle for fighting terrorism or wading more deeply into Syria. The critique predates the Paris attacks and the Turkish downing of the Russian plane, but both incidents throw the limits of the alliance into sharp relief.

“It does say something of where NATO is now that it is not a relevant tool for collective defense again terrorism or even a relevant tool for crisis management or airstrikes against [Islamic State],” said a French official.

In the immediate aftermath of the Paris attacks, both Democrats and Republicans in the U.S. began saying the alliance should invoke its collective defense clause.

But officials in Paris decided not to invoke NATO, and instead invoked, for the first time, a European Union defense provision: Article 42-7 of the Lisbon treaty.

French and NATO officials said they opted to use the EU treaty because the kind of capabilities they wanted help with—police, border security, law enforcement intelligence—were, for the most part, not external military matters.

France told its international partners that the country hoped to press the EU to make more progress on tracking passenger names and beefing up the external borders of Europe. French officials also said that using the EU treaty would help them avoid debt-level restrictions imposed by Brussels as Paris beefed up security spending.

The senior alliance official said NATO’s treaty focuses on a collective response, while the EU treaty allows France to ask individual nations for specific help.

“They like the flexibility of 42-7, which focuses on a bilateral approach,” said the senior NATO official. “This has France in the driver’s seat asking for targeted support.”

For now, U.S. officials also want to avoid a direct alliance role in the fight against Islamic State. Political disagreements within the alliance over who to partner with in Syria—and, more specifically, Turkey’s distrust of Syrian Kurdish forces—mean bringing the alliance under direct oversight would complicate matters.

But U.S. and alliance officials said there could eventually be room for a broader NATO role in Syria.

NATO has put forth an immense effort over the past year into building up a rapid-reaction force that could be used to counter Russian aggression. The alliance is also making sure that a new spearhead task force—known as the VJTF—could be ready for deployment in North Africa or the Middle East, not necessarily for direct intervention but to help with training efforts.

“NATO has to face all the threats,” said Gen. Denis Mercier, who helps develop the alliance’s future capabilities as the Supreme Allied Commander Transformation.

“All the tools we develop, and this is especially true for the VJTF, must be suitable for the threats coming from the south and terrorism.”

In the long term, officials said, the alliance could expand its training missions in Jordan and Iraq and take a more direct role in countering Islamic State.

“We should expand those with an eye to an eventual assumption from the coalition of the train, advise, and equip mission,” said a senior NATO official. “Look at who is on the ground doing the training, it is all NATO allies.”

Ian Kearns, the director of the European Leadership Network, says the decision by France not to invoke the NATO treaty doesn’t mean the alliance is irrelevant, but shows that it is not seen “as the vehicle of choice to address every security threat.”

“This is a sign of an ever more diverse and complex security environment that no single state or organization can handle,” he said.

NATO has long been focused on deterrence. Gen. Mercier, the highest-ranking French general in NATO, said it is easier to deter state actors than terrorists. But by focusing on building partnerships in the Middle East, the alliance can adapt and remain relevant.

“We can adapt NATO’s posture to fit all the threats of the 21st Century,” Gen. Mercier said. “The main thing is to fight terrorism at its source. To fight terrorism at the source we have to develop partnerships.”