Mr. Biden said that if there was an “imminent threat” that warranted this “extraordinary action,” Americans should receive “an explanation and the facts to back it up.”

“At precisely the moment when we should be rallying our allies to stand beside us and hold the line against threats, Donald Trump’s shortsighted, ‘America First’ dogmatism has come home to roost,” Mr. Biden said. He went on to add, “We are alone now. We’re alone and we’ll have to bear the cost of Donald Trump’s folly.”

On the campaign trail, Mr. Biden has emphasized his decades-long record in international affairs and extensive relationships abroad, highlighting a contrast with his rivals in the Democratic field, who have largely been focused on domestic matters throughout the race. In New York, the setting appeared designed to conjure the White House briefing room: Mr. Biden spoke against a blue backdrop before a room full of reporters. He walked in to the clicking of multiple cameras and offered his own prescription for the path forward, calling for “cleareyed, hard-nosed diplomacy grounded in a strategy that’s not about one-off decisions and one-upsmanship.”

“Mr. President,” he urged, “you have to explain your decision and your strategy to the American people. That’s your job as president, Mr. President. Not ‘Dear Leader.’ Not ‘Supreme Leader.’ Democracy runs on accountability, and nowhere is it more important than the power to make war and bring peace.”

Mr. Biden, who has faced renewed scrutiny of his foreign policy record and especially his Iraq war vote, also appeared to misspeak at times, referring to Iran when he apparently intended to say Iraq, and he appeared to say that the current perilous situation was “unavoidable,” when excerpts from the speech circulated before the appearance used the word “avoidable.”

Still, Mr. Biden’s advisers and allies hope that the gravity of the moment will further crystallize the importance of defeating Mr. Trump in the minds of voters, and polls continue to show that Democrats believe Mr. Biden has the best chance to do so, though other candidates have also polled strongly against the president in hypothetical head-to-head matchups.

The current crisis “just reinforces how high the stakes are in this election,” Mr. Biden said at a fund-raiser earlier Tuesday, during which he also envisioned a Senate dynamic in which one could see “Mitch McConnell changing some ideas or being more — how can I say — mildly cooperative,” even as Mr. Biden also discussed the imperative for Democrats to win back the Senate, revoking Mr. McConnell’s title as majority leader.