President Barack Obama is using his last day in Europe to renew his quest for foreign support for a U.S. military strike in Syria. But three days after he left Washington, it's unclear whether the global coalition the president has been seeking is any closer to becoming a reality.

China's a firm no. The European Union is skeptical about whether any military action can be effective. Even Pope Francis weighed in, urging leaders gathered here to abandon what he called a "futile mission."

Still, Obama was undeterred. As the president pressed his case on the world stage, he was dispatching his U.N. ambassador, Samantha Power, to a Washington think tank to argue that the global community cannot afford the precedent of letting chemical weapons use go unpunished.

A key status update was to come Friday when Obama, his diplomatic dexterity pushed to the max, will be quizzed by reporters in the waning hours of the Group of 20 economic summit in this Russian port city. Meanwhile, the White House was assuring allies it was seeking diplomatic and political support for a Syria strike — not necessarily direct military involvement.

A jobs-and-growth agenda awaiting world leaders gathering at the ornate Constantine Palace quickly gave way to intense posturing over Syria — at least on the surface. The leaders served up Syria as dinner conversation Thursday at the suggestion of the summit's host, Russian President Vladimir Putin.

A fleeting interaction between Obama and Putin became the high-drama moment of the summit, underscoring the labored state of relations between the two leaders who stand on opposing sides of the Syrian conflict. Russia has steadfastly backed Syrian President Bashar Assad — militarily, economically and diplomatically — and disputes claims that Assad's regime was behind chemical attacks that the U.S. says killed more than 1,400 Syrians. Other estimates are lower.

In public, at least, the Russian and the American were all smiles Thursday, making small talk in front of news cameras for a few seconds as Obama arrived at the summit. But the welcoming handshake may have been where the pleasantries ended.

Putin's spokesman, Dmitry Peskov, said a U.S. strike would "drive another nail into the coffin of international law." Meanwhile, the Kremlin said Russia was boosting its naval presence in the Mediterranean Sea, moving in warships "primarily" for a possible evacuation of Russians from Syria.

Before his scheduled return to Washington late Friday, Obama was to meet with French President Francois Hollande, his strongest ally when it comes to Syria, and Chinese President Xi Jinping. He also planned to meet with Russian lesbian, gay, bisexual and transgender activists, calling attention to another area of disagreement with Moscow.

Even at home, there was far from a consensus that an American strike on Syria was the best course of action. Awaiting Obama upon his return was an equally fractious debate in Congress over whether to authorize the limited military action he was proposing.

Pulling out all the stops, Obama was working the phones from Europe and appealing for support from leery lawmakers, Democratic and Republican alike. And he called off a planned trip to California next week, opting to stay in Washington to keep up the pressure on Congress to say yes.

As top national security officials continued to brief Congress on the accusation against Assad and the proposed response, a measure authorizing Obama to act was advancing tenuously through the Senate, winning approval from a foreign relations panel Wednesday and heading to the Senate floor. The measure's prospects were dicier in the Republican-controlled House.

"We're very pleased with the trend lines," Ben Rhodes, Obama's deputy national security adviser, said.

The fierce domestic debate over a Syria strike offered a prelude to grueling days ahead as Obama and Congress brace for major clashes over the nation's finances, immigration and other pressing issues. When lawmakers return next week from their annual summer recess, Syria will compete with critical, looming deadlines to raise the nation's borrowing limit and approve spending to avoid a government shutdown.