As he touched down in St. Petersburg on Thursday morning, President Obama greeted his host Vladimir Putin with a handshake and a smile.

But the cordial greeting belies the tinderbox the two leaders are sitting on, as they posture and deliberate over a potential U.S. strike on Syria -- one of Russia's closest Mideast allies.

Putin escalated concerns about the fallout from any strike when he indicated in an interview published Wednesday that his country could send Syria and its neighbors in the region the components of a missile shield if the U.S. attacks.

U.S. Gen. Martin Dempsey, chairman of the Joint Chiefs of Staff, testified this week that the Russians might even replace any military assets the U.S. destroys in a strike.

The warnings raise the possibility of a supposedly "limited" strike on Syria turning into a proxy tit-for-tat between Russia and the U.S.

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Rep. George Holding, R-N.C., went further during a hearing on Syria on Wednesday, pressing military officials on what the U.S. would do "if Russia decided to strike at us in that theater."

"We can certainly say that Russia would have options to strike us in that theater in retaliation for us striking their ally," he warned.

Dempsey declined to engage in that discussion, saying only that "Russia has capabilities that range from the asymmetric, including cyber, all the way up through strategic nuclear weapons. And again, it wouldn't be helpful in this setting to speculate about that."

Secretary of State John Kerry, though, said the Russians have made clear they don't intend to go to war over a strike on Syria.

Perhaps more likely is that Putin's government would continue to aid and prop up the Assad regime, undermining any gains made by a U.S. strike.

"Putin will live up to what he says," Fox News military analyst retired Lt. Col. Ralph Peters said." If we destroy Syrian military technology, Putin will replace it."

Putin said in a published interview this week that he'd reconsider the status of a suspended S-300 missile defense contract.

"We have a contract for the delivery of the S-300s. We have supplied some of the components, but the delivery hasn't been completed," he said. "We have suspended it for now. But if we see that steps are taken that violate the existing international norms, we shall think how we should act in the future, in particular regarding supplies of such sensitive weapons to certain regions of the world."

The possibility for Russia stepping up its role in the region makes Obama's visit to Russia all the more critical. Though the president has nixed a formal one-on-one sitdown with Putin during the G-20 summit, he is expected to speak with the Russian leader on the sidelines. Though he said Wednesday that U.S.-Russian relations have "hit a wall," he said he'd continue to engage Putin.

"It is not possible for Mr. Assad to regain legitimacy in a country where he's killed tens of thousands of his own people," Obama said. "So far, at least, Mr. Putin has rejected that logic."

Obama added: "I'm always hopeful, and I will continue to engage him."

Obama's challenge to change Putin's mind comes as China warns that any military action against Syria will push up oil prices and hurt the world economy.

Speaking in St. Petersburg Thursday, Chinese Vice Finance Minister Zhu Guangyao said that "Military action would have a negative impact on the global economy, especially on the oil price -- it will cause a hike in the oil price," before citing estimates that a $10 rise in oil prices could push down global growth by 0.25 percent. Guangyao also urged a U.N.-negotiated solution to the chemical weapons standoff. Like Russia, China is a major arms supplier to Syria and holds veto power over any Security Council resolution.

The White House went out of its way to say Obama would not hold bilateral discussions with the Russian leader while in St. Petersburg. Instead, Obama will formally meet on the summit's sidelines with the leaders of France, China and Japan, though a senior administration official said the two presidents will have a chance to speak.

Russia's resistance is a key reason why the U.N. Security Council so far has not gotten on board with U.S. calls for action in response to the alleged chemical weapons strike against Syrian rebels on August 21.

Putin has been among the loudest critics on the international stage of Obama's push for a military strike in Syria. He reportedly blasted the push on Wednesday as an "act of aggression." He has said in recent interviews that a strike would be illegal if the United Nations does not support it.

The president said Wednesday there was far more than his own credibility at stake in responding to the chemical weapons attack.

"I didn't set a red line, the world set a red line," he said. "The world set a red line when governments representing 98 percent of world population said the use of chemical weapons are abhorrent." He added that Congress set its own red line when it ratified the treaty.

With Obama in Europe, his top national security aides were to participate Wednesday in public and private hearings at the Capitol to advance their case for limited strikes in retaliation for what the administration says was a deadly sarin gas attack by Assad's forces in the eastern suburbs of Damascus.

The Senate Foreign Relations Committee voted 10-7 with one abstention to authorize the use of force against Syria Wednesday, the first in a series of votes as the president's request makes its way through Senate and House committees before coming before the two chambers for a final vote, probably sometime next week.

The Associated Press contributed to this report.