BAGHDAD (AFP) - Syria's neighbors are bracing for an influx of refugees fleeing their country in fear of U.S.-led military action, compounding what the UN has branded a "disgraceful humanitarian calamity."

The movement could deepen an already enormous regional refugee crisis.

The numbers of Syrians seeking safety abroad have increased nearly 10-fold from a year ago, the latest grim milestone in a 29-month battle between President Bashar al-Assad and rebels bent on overthrowing him.

Correspondents and witnesses, meanwhile, have reported an even greater exodus of Syrians into neighboring countries since U.S. President Barack Obama warned last week he was ready to launch military strikes on Assad's regime over its alleged use of chemical weapons.

"If something happened -- if there were airstrikes, if there was another chemical attack -- the first reaction would be for people to flee," said Muriel Tschopp, deputy director for emergency responses for the International Rescue Committee.

"A lot of governments that have been generous until now, they also see that it's not sustainable. They were ready for a six-month crisis, a one-year crisis. They were not ready for a three-year crisis, or an entire country emptying out."

The U.N.'s refugee agency said from Geneva on Tuesday that more than two million Syrians had fled the country, up from about 230,000 a year ago, lamenting that Syria was "hemorrhaging women, children and men who cross borders often with little more than the clothes on their backs."

"Syria has become the great tragedy of this century," said UN refugee chief Antonio Guterres, adding that it was "a disgraceful humanitarian calamity with suffering and displacement unparalleled in recent history."

And now, foreign governments are increasingly having to prepare for potentially even more Syrians in search of safety outside of their country.

"If the security situation in Syria gets worse, the refugees will continue to come, especially if Syria is targeted," said Dindar Zebari, deputy chief of the Iraqi Kurdish foreign affairs department.

He added that the Kurdish region's "doors are open for them" but noted that "the huge number of refugees creates a problem for our budget, which is limited."

On Saturday, Jordan's committee tasked with dealing with refugees crossing from Syria discussed expanding the already massive Zaatari camp, and establishing an entirely new site for incoming Syrians.

The plans from Jordan, which already hosts around a half-million Syrian refugees, would see Zaatari's capacity increased from around 130,000 now to about 150,000, but there are few details about the proposed new camp.

Turkey, meanwhile, says it is "prepared in the face of a refugee influx," according to Mustafa, spokesman for the country's Disaster and Emergency Management Directorate.

"We have the capacity to build the camps," he said, adding that Turkey's open-door policy towards Syrian refugees would remain in place in the event of a major exodus sparked by possible intervention.

Past experience in the region suggests, however, that the refugee impact from the strikes could be limited, according to UNHCR spokesman Peter Kessler, who was in Jordan ahead of the US-led invasion of Iraq a decade ago.

"At the time, of course, the UN was preparing for a major exodus from Iraq, and pre-positioning supplies throughout the region," Kessler said.

But the refugee flow "never happened in the immediate aftermath of the airstrikes around Baghdad and elsewhere in Iraq."

"There were, of course, a great many Iraqi refugees starting to flee six months later, due to the security problems that arose, but the number of people that fled (immediately following the invasion) were in the low thousands."

Kessler noted that the UN maintained key stockpiles of emergency supplies for refugee and other crises around the Middle East, with another global stockpile in Dubai.

"I don't have a crystal ball -- nobody does," he said. "We'll just have to wait and see."