(CNN) -- It's supposed to be a summit about the global economy, but the debate over possible military strikes for Syria's apparent use of chemical weapons is already overshadowing the G-20 conference this week.

The meeting in Russia will pit two leaders with polar opposite views on Syria -- U.S. President Barack Obama, who wants to launch limited military strikes against the Syrian regime, and Russian President Vladimir Putin, whose country stands by its longtime ally in the Middle East.

The views of the 18 other countries at the G-20 run the gamut -- but could be influenced by whatever happens in St. Petersburg.

Global chess pieces

Calls for intervention in Syria intensified after an alleged chemical weapons attack in rebel strongholds last month left about 1,400 people dead, according to U.S. estimates. Obama has been at the forefront of calls for a military response, along with French President Francois Hollande.

But some world leaders took the summit spotlight to stump against military action.

European Council President Herman Van Rompuy said that while the international community "cannot remain idle" in the face of Syria's apparent chemical weapons use, "there is no military solution to the Syrian conflict."

"Only a political solution can end the terrible bloodshed, grave violations of human rights and the far-reaching destruction of Syria" he said. "Too many lives have already been lost and too many people have suffered for too long and lost too much."

Pope Francis also spoke out, sending a letter Thursday to Putin in his role as host of the G-20 summit, urging a peaceful solution to the Syrian crisis and calling military intervention a "futile pursuit."

"Rather, let there be a renewed commitment to seek, with courage and determination, a peaceful solution through dialogue and negotiation of the parties, unanimously supported by the international community," Francis wrote. "Moreover, all governments have the moral duty to do everything possible to ensure humanitarian assistance to those suffering because of the conflict, both within and beyond the country's borders."

More debate

The French parliament is expected to debate military action against Syria this week. But there's not a lot of nationwide support for such an intervention -- only one in three people in France endorses punishing Syria.

President Francois Hollande will wait to hear the decision by the U.S. Congress on whether Washington will take military action on Syria before he addresses the French public directly, Foreign Minister Laurent Fabius told CNN affiliate France 2 Thursday.

But France and the rest of the world will have to wait; the U.S. Senate isn't expected to vote on a resolution for targeted military strikes until next week.

Britain, normally a dependable U.S. ally in military affairs, has voted against taking any military action.

Can the U.S. and Russia get on the same page?

Obama arrived in St. Petersburg at 2:06 p.m. (6:06 a.m. ET). He has no formal meetings scheduled with Putin, but Deputy National Security Adviser Ben Rhodes told reporters aboard Air Force One that the president will likely have opportunities to talk with the Russian leader during the meetings.

Obama will talk with allies about his position on Syria, but U.S. officials don't expect every country will fall in line with the president's proposal, Rhodes said.

Lakhdar Brahimi, the joint U.N.-Arab League envoy to Syria, also left for the G-20 summit Thursday to try to make a dent in the global diplomatic impasse.

Brahimi, whose plan for a Syrian cease-fire fell apart, is hoping to meet with Obama and Putin to push for new peace talks for Syria, spokeswoman Khawla Mattar said.

But both Russia and the United States have stood firm on stances toward Damascus.

Russia, a longtime arms supplier to Syria, has vetoed every attempt at the U.N. Security Council to act against its ally.

But on Wednesday, Putin said he "doesn't exclude" backing a U.N. resolution for military action -- as long as there is undeniable proof Syria's government was behind the August 21 attack.

The United Nations is waiting for test results from samples taken from Syria that could indicate whether a chemical weapon attack took place. But the U.N. investigation won't conclude who was responsible.

The Obama administration has said independent tests revealed "signatures of sarin" gas in blood and hair samples from Syria, and charge that there is no doubt President Bashar al-Assad's regime was behind the attack.

Obama is expected to make a push for why the world needs to take action after the alleged chemical weapons attack.

"My credibility isn't on the line. The international community's credibility is on the line," Obama told reporters before flying to Russia.

"The moral thing to do is not to stand by and do nothing."

But if he doesn't muster more international support, the United States might strike on its own. Unlike the case of Libya in 2011, there is no U.N. Security Council agreement, nor is there a NATO-backed mission against Syria.

Warning from Syria

Syrian presidential adviser Bouthaina Shaaba warned that anyone who might strike without U.N. backing would pay a steep price.

"The Syrian people will never leave, they will always be here," Shaaban said Wednesday on Britain's Channel 4. "But those who lead the aggression will leave, and they will (live with) the results of this aggression."

Iran also said it will defend Syria at any cost.

"We will support Syria to the end," Revolutionary Guard commander Gen. Qassem Soleimani said.

The United Nations estimates more than 100,000 people have been killed in Syria since 2011, when peaceful demonstrations against the regime were met by a fierce government crackdown. The ensuing chaos spiraled into a civil war, with scores of deaths reported every day.

More than 2 million Syrians have fled their country, the U.N. refugee agency says, and more than 4 million are internally displaced.

CNN's Jim Acosta, Samira Said, Chris Lawrence and Pierre Meilhan contributed to this report.