Eleven thousand Syrians have fled the country in the past 24 hours, the UN says.
Nine thousand Syrians fled to Turkey, while 1,000 went into Jordan and 1,000 into Lebanon just in one day, Panos Moumtzis, the UN refugee agency's co-ordinator for the region, told reporters in Geneva.
He said the estimated figures are "really the highest we have had in quite some time" compared with an average 2,000 to 3,000 Syrians fleeing daily.
They bring the number of Syrian refugees registered with the agency to more than 408,000.
Radhouane Nouicer, the UN's regional humanitarian co-ordinator for Syria, said after an international meeting on Syrian humanitarian aid that the country is seeing unrelenting increases in violence.
Earlier, reports said a group of Syrian soldiers, including two generals and 11 colonels, had fled to Turkey with their families seeking refuge and were taken to a camp that shelters military defectors.
The group of 71 people arrived in Hatay, said Turkey's state-run Anadolu Agency.
Meanwhile Syria's president Bashar Assad said his country is not in a state of civil war, and that he has no regrets about any decisions he has made since the uprising against him began nearly 20 months ago.
Instead of civil war, Mr Assad said, Syria is facing "terrorism through proxies," referring to foreign backing of the rebellion against his regime.
Syria's uprising began in March 2011 as mostly peaceful protests against Mr Assad's rule, but as rebels took up arms in the face of a bloody repression of the protests, the conflict morphed into a civil war. The fighting has taken on grim sectarian tones, with the predominantly Sunni rebels battling government forces loyal to a regime dominated by minority Alawites, an offshoot of Shiite Islam.
Anti-government activists say more than 36,000 people have been killed for far, including thousands of government troops. Several hundred thousand Syrians have fled to Jordan, Turkey, Egypt, Lebanon and Iraq.
"We do not have a civil war," Mr Assad said in an interview with the English-language Russia Today TV. "It is about terrorism and the support coming from abroad to terrorists to destabilise Syria. This is our war."
"It is a new kind of war; terrorism through proxies, either Syrians living in Syria or foreign fighters coming from abroad. So, it is a new style of war, this is first and you have to adapt to this style and it takes time, it is not easy."
He acknowledged his troops are fighting a "tough war and a difficult war," adding that when foreign countries stop sending arms to rebels, "I can tell (you) that in weeks we can finish everything."
Asked if he has any regrets, he said: "Not now," although he acknowledged that "when everything is clear" it would be normal to find some mistakes.