It was the highest monthly figure since the conflict erupted in March last year, UNHCR spokeswoman Melissa Fleming told reporters.
"This is a significant escalation in refugee movement," she said, adding that the total number of refugees who have been registered or are awaiting registration in neighbouring countries now stood at 235,000.
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"This probably points to a very precarious... situation in the country," she said, adding: "We're responding as best we can."
The agency said some 1,000 Syrian refugees were crossing into Jordan each day, while Iraq was now seeing a steep hike in the number of Syrian Kurds arriving in the country, with about 500 crossing daily.
Iraqi refugees have also been fleeing Syria by the hundreds, the UNHCR said, adding that while most were leaving due to the overall security situation, some had reported being directly threatened.
A taxi used by Iraqi families to return to Iraq was hijacked at the weekend, while three Iraqi refugees were killed last week in a Damascus suburb, the agency said.
Lebanon has taken in around 59,000 Syrians to date, while Ankara says there are more than 80,400 Syrian refugees in Turkey, with around 8,000 reportedly still waiting to cross.
The UNHCR said it has launched a programme aimed at helping displaced Syrian families financially, which it said was the "most effective way of supporting vulnerable families in the constrained security environment in much of Syria."
The agency said it had handed cheques to 730 Syrian families so far, adding that it and the Syrian Arab Red Crescent hoped to give financial help to 35,000 families, or some 200,000 people, in the coming months.
According to the Syrian Observatory for Human Rights, over 26,000 people have been killed since the revolt began in March last year -- more than two-thirds of them civilians.
