“It could raise grave doubts about the credibility of the American security guarantee and provide Russia with an incentive to probe vulnerable Baltic States,” Thomas Wright, a Brookings Institution scholar, wrote last week, before Mr. Trump began his first foreign trip as president.

The NATO leaders who will meet on Thursday face other difficult questions as well, including how many troops the United States will contribute to replenish the alliance’s forces fighting in Afghanistan. Right now, the international security force assisting the Afghan Army has about 13,000 troops; about 8,400 of them are American. Mr. Trump is considering proposals to send as many as 5,000 more, including Special Operation forces.

Mr. Trump is scheduled to speak Thursday afternoon at NATO’s new headquarters, a gleaming $1.2 billion facility that he will help dedicate with a part of the World Trade Center in New York that was destroyed in the Sept. 11 attacks.

The alliance invoked Article 5 the next day, telling the United Nations on Sept. 12, 2001, that if the attack had come from outside the United States, it would be covered by the mutual defense pact. NATO later affirmed that decision when Al Qaeda was identified as the group responsible.

“By invoking Article 5, NATO members showed their solidarity toward the United States and condemned, in the strongest possible way, the terrorist attacks against the United States,” the alliance says on its website.

Endorsing Article 5 would align Mr. Trump with every previous American president since the treaty was signed. All of them publicly reaffirmed that the United States would come to the aid of a NATO member that came under attack. But it would follow more than a year of criticism and complaints by Mr. Trump that NATO was taking advantage of the United States and that other member states were not pulling their weight.

In a March 2016 interview with The Times, Mr. Trump said that NATO was obsolete, that Russia was no longer the threat it had once been, that other NATO nations were not contributing their fair share, and that they were not fighting terrorism as aggressively as the United States does.