U.S. President Barack Obama and his Russian counterpart, Vladimir Putin, said they held "constructive" talks Friday on the deeply divisive issue of Syria on the sidelines of the Group of 20 summit in Russia.

The two leaders hold opposing views over whether military action should be taken against the Syrian government over its alleged use of chemical weapons on its own people.

Obama is seeking to rally domestic and international support for military strikes on Syria, while Putin -- a determined ally of Syrian President Bashar al-Assad -- has challenged the assertion that regime forces were behind the attacks. Syria's government blames rebel forces.

Obama said the two leaders had a "candid, constructive" conversation but acknowledged that Putin was unlikely to shift his position on military action against Syria.

However, he said, they could both agree to work toward a political resolution to the crisis.

Putin gave a similar account of their meeting. "He doesn't agree with me, I don't agree with him. But we listened to each other," Putin told reporters.

He and Obama also talked about ways to solve the Syrian crisis peacefully, he said.

Obama said he believed the majority of the leaders at the G20 meeting were "comfortable with (the) conclusion that the Assad government was responsible" for the use of chemical weapons last month.

But, he said, divisions arose over whether military action against Syria must be authorized by the U.N. Security Council, where Russia has blocked action so far.

Obama said that because of Security Council "paralysis" on the issue, countries should be willing to act without the council's authorization.

Obama: World cannot stand idly by

"If we are serious about upholding a ban on chemical weapons use, then an international response is required, and that will not come through Security Council action."

But he said he was encouraged by the discussions about Syria in St. Petersburg. "There's a growing recognition that the world cannot stand idly by," Obama said.

The U.S. president showed emotion as he talked of the gassing of more than 1,400 people in Syria, 400 of them children.

"This is not something we fabricated, this is not something we are using as an excuse for military action. ... I was elected to end wars, not start them," he said. "But we have to make hard choices when we stand up for things we care about."

Putin said the leaders gathered in St. Petersburg were split nearly "50-50" regarding whether to intervene militarily in Syria.

He stressed that action against Syria without U.N. Security Council approval would be illegal.

The Syrian government has said that opposition fighters launched the August 21 chemical attack on the outskirts of Damascus.

The United Nations has said more than 100,000 people -- including many civilians -- have been killed since a popular uprising spiraled into a civil war in 2011.

Tensions affect U.S. staff in Lebanon, Turkey

As tensions ratchet up over Syria, the U.S. State Department on Friday ordered the withdrawal of nonessential personnel from the U.S. Embassy in Beirut, Lebanon, and authorized nonemergency staff to leave a consulate in Adana in southern Turkey.

"Given the current tensions the region, as well as potential threats to U.S. Government facilities and personnel, we are taking these steps out of an abundance of caution to protect our employees and their families, and local employees and visitors to our facilities," a statement said.

Many observers fear that the civil war in Syria, which has become increasingly sectarian in nature, could spill over into neighboring countries, some of them already politically fragile.

The State Department also issued revised travel warnings Friday for Lebanon and Turkey, both of which share a border with Syria.

It urges U.S. citizens to "avoid all travel to Lebanon because of current safety and security concerns" and to be "alert to the potential for violence" if traveling to or living in Turkey.

Many in Lebanon worry that the involvement of the Lebanese Shiite militant group Hezbollah in Syria's civil war could destabilize their nation.

Lebanon has been shaken by a series of deadly bombings in recent weeks, including a blast in a Hezbollah stronghold in Beirut.

Al-Assad warned this week that a regional war could break out if Syria is attacked.

"The Middle East is a powder keg, and the fire is approaching today," he told French newspaper Le Figaro in an interview Monday.

Obama pushes for congressional action

Obama is seeking congressional approval for possible U.S. military strikes against Syria, although no vote is expected until after lawmakers reconvene from recess on Monday.

The president said Friday that some skepticism from lawmakers, including his own Democrats, and the wider public was not unexpected.

He knew it was going to be "a heavy lift" when he announced Saturday that he was putting the proposal before Congress, he said, with some lawmakers foreseeing a "slippery slope" toward a prolonged U.S. involvement in Syria.

"For the American people who have been through over a decade of war now, with enormous sacrifice of blood and treasure, any hints of further military entanglement in the Middle East are going to be viewed with suspicion," Obama said. "That suspicion will probably be even stronger in my party than in the Republican Party."

The Syrian parliament has urged the U.S. House of Representatives not to support the proposed U.S. military action, the country's state news agency, SANA, said Friday.

In a letter addressed to U.S. House Speaker John Boehner, his Syrian counterpart, Jihad al-Laham, called upon the House to communicate through civilized dialogue, not blood and fire, the news agency said.

He also stressed that Islamic extremist fighters have seized and possess chemical weapons, SANA reported.

Boehner and House Majority Leader Eric Cantor have both backed Obama, but Boehner has said it is up to the White House to get the votes. Obama needs at least 217 votes to secure his resolution there.

According to CNN's count, 109 House members plan to vote "no," while 23 -- including a number of high-profile Republicans -- plan to back it. More than 280 representatives remain undecided.

Diplomatic debate

Questions over exactly what happened in Syria and the appropriate response have dominated international diplomacy for two weeks.

The European Union's defense ministers on Friday condemned the use of chemical weapons in Syria and said "many signs" pointed to the Assad regime being the culprit.

"All member states have denounced the use of chemical weapons and those responsible for this attack should bear the responsibility and there are many signs that allow us to conclude that the chemical weapons were used by the regime," said Lithuanian Defense Minister Juozas Olekas.

The issue has overshadowed the G20 summit in St. Petersburg, where discussions would usually focus on global economic matters.

Ben Rhodes, U.S. deputy national security advisor for strategic communications, told journalists in St. Petersburg on Friday that Syria had dominated a working dinner Thursday night at the summit.

"I think there is broad agreement here that chemical weapons were used, and that that's a significant challenge for the international community," he said.

"Similarly, we believe a majority of the countries accept the basic premise that Assad was responsible, so therefore he and his regime are the accountable actors in this instance."

Syria offers rewards

Meanwhile, Syrian authorities are offering rewards, amounting to nearly $4,400 for handing over non-Syrian "terrorists," Syrian state TV said Friday. The Syrian government often refers to rebels as terrorists.

There is also a reward of nearly $1,800 for reporting the whereabouts of these individuals or providing help leading to their arrest, according to the state broadcaster.

The identity of those providing information would remain confidential, and they would be provided with protection, state TV said.

CNN's Barbara Starr, Jason Hanna, Hamdi Alkhshali and Richard Allen Greene contributed to this report.