When Turkey destroyed a Russian warplane it had warned away from its airspace, the fallout threatened to destroy chances for any grand coalition of international powers to change the course of chaos in Syria, at least for now.

The fatal incident in the skies Tuesday immediately escalated, and complicated, what had already been an intensely difficult enterprise—trying to bridge divides and corral longtime adversaries into a pact to combat their one shared enemy, Islamic State.

The Turkish-Russian aerial altercation quickly hardened the positions held by all sides. While the U.S. and its ally France dug in on their demands on resolving the Syrian conflict, Russia and its ally Iran adhered to theirs.

Aggravating the conflict was a war of words, with Russian President Vladimir Putin leveling charges that Turkey, an ally of the U.S. and France, finances terrorism—accusations widely aired on Russian television in a daylong propaganda blitz.

Amid the strife, President Barack Obama and French President François Hollande presented a united front, speaking at the White House Tuesday after their first meeting since the Paris attacks. They outlined changes they said Russia must make to its military strategy in Syria and to its position on a political resolution to the conflict before the U.S.-led coalition, which includes Turkey, would cooperate with Moscow in the fight against Islamic State.

The demands made by the U.S. and French leaders—including the key issue of the future of Syrian President Bashar al-Assad, whom Russia supports—now have set the stage for a tense meeting between Mr. Hollande and Mr. Putin scheduled for Thursday.

The downing of the Russian jet is likely to redraw the lines of engagement in Syria and affect Russians’ perceptions of their country’s intervention, analysts say.

“Hollande’s mission was to reach some kind of coordination with Russia,” said Alexei Makarkin, deputy director at Center for Political Technologies. “Now it is very, very doubtful that it is even possible to coordinate actions. The maximum that we can talk about now is avoiding shooting each other.”

Mr. Hollande’s visit to Moscow this week was supposed to be a crowning moment for Mr. Putin’s plan to bring more countries into his antiterrorism tent, as well as any potential rapprochement with the West after isolation over his intervention in Ukraine and annexation of Crimea.

But Mr. Obama, after expressing a new openness to coordinating with Russia since he met with Mr. Putin in Turkey last week, on Tuesday sought instead to isolate him.

“Russia right now is a coalition of two—Iran and Russia, supporting Assad,” he said. “We’ve got a global coalition organized. Russia is the outlier.”

At the same time, the U.S. and French leaders sought to demonstrate enhanced cooperation in their coalition.

Mr. Hollande said the immediate priority in the military campaign in Syria is to take back territory currently controlled by Islamic State and secure the border with Turkey.

Mr. Obama called on the European Union to implement an agreement that would require airlines to share passenger information.

“By targeting France, terrorists were targeting the world,” said Mr. Hollande.

Mr. Hollande’s stop in Washington was part of a whirlwind international tour to build a “single, grand coalition” of nations to take on Islamic State, which he called for last week.

French diplomats, however, have in recent days inched away from Mr. Hollande’s call for such a sweeping coalition. Instead officials in Paris have spoken of “coordination” in the strikes against Islamic State and have ruled out any shared command center for bombing targets in Syria.

The subtle shift suggested hopes had dimmed, even before the Russian fighter was shot down, that the Paris attacks would become a catalyst for a breakthrough in broader international military and political cooperation,

Mr. Hollande appeared to reassure the White House that following the Paris attacks he hadn’t elevated the military campaign against Islamic State above holding fast to France’s position that Mr. Assad must exit.

“We cannot imagine the Syrians getting together, gathering around the leader who is responsible for most of the 300,000 deaths in a few years,” Mr. Hollande said, adding that a political resolution “must lead to Assad’s departure.”

Mr. Obama expanded his view of what constitutes Mr. Assad’s exit, suggesting simply that his “choosing not to run” in another election would be enough for the U.S. to agree to a political resolution to the Syrian conflict.

Mr. Putin, meanwhile, in Tehran Monday, reaffirmed his support for Mr. Assad.

Disagreements over whether Mr. Assad should remain in power—and, if so, for how long—have emerged as the main obstacle not only to a political resolution under negotiations in Vienna, but also to a broad military coalition that includes Russia.

Mr. Obama stood by Turkey and said the downing of the Russian jet was more evidence against Mr. Putin’s strategy in Syria of targeting all opponents of Mr. Assad, rather than just Islamic State.

“This points to an ongoing problem with the Russian operations in the sense that they are operating very close to a Turkish border, and they are going after a moderate opposition that are supported by not only Turkey but a wide range of countries,” Mr. Obama said.

Mr. Hollande said it “means that we must find a solution to the Syrian crisis, because we can see what the risks are otherwise.”

The Russian leader on Tuesday accused Turkey of funding Islamic State through oil purchases that could amount to hundreds of millions of dollars.

“We long ago established the fact that a large amount of oil and oil products enter Turkey from territory seized by Islamic State, which represents a large monetary replenishment for the group,” Mr. Putin said on Russian state television.

Russian state news broadcasts emphasized the accusation. “Many experts say Turkey has long supported extremists in one way or another,” began one of the segments that aired on the First Channel.

The exchanges seem certain to poison any chance of a single coalition, with the U.S. refusing to abandon its partner Turkey while Mr. Putin making any Russian alliance that included Ankara unthinkable

Foreign Minister Sergei Lavrov said he was canceling his trip to Istanbul on Wednesday, where he had planned to meet with his Turkish counterpart.

Mr. Putin didn’t outline retaliatory steps, but analysts said some measures were to be expected.

Vasily Kashin, an analyst at Moscow-based defense think tank CAST, said Russian jet fighters may increasingly turn their attention to Syrian rebel groups supported by Turkey, including the Turkmen.

“No one will attack a NATO country and a significant military power, but the talks over the future of Syria and the billions of dollars in trade relations are likely to suffer consequences,” said Mr. Kashin. Turkey is a major customer for Russian energy and a popular destination for Russian vacationers.

Added Mr. Kashin: “Russia will likely expand its operations in a way that will directly negatively affect Turkish interests on the ground.”