Some 294,000 refugees have already left Syria, and the UNHCR is appealing for money to help deal with the crisis.
Most of the refugees are housed in camps in Turkey, Lebanon and Jordan.
Rami Abdel Rahman, from the Syrian Observatory for Human Rights (SOHR), said the figure included only those whose names had been documented.
“If we count the unidentified bodies, the figure will be much higher,” he said.
The observatory (SOHR) said 199 of Wednesday’s dead were civilians.
The SOHR is one of the most prominent organizations documenting and reporting incidents and casualties in the Syrian conflict. The group says its reports are impartial, though its information cannot be independently verified.
Other groups estimated Wednesday’s death toll to be considerably higher.
The UNHCR said between 2,000 and 3,000 refugees were fleeing the violence into neighboring countries every day.
“Many refugees are arriving with only the clothes on their backs,” said Panos Moumtzis, the agency’s regional co-ordinator for Syrian refugees.
“Some have been displaced many times before leaving Syria. They need humanitarian assistance from day one.”
The agency said in March it estimated that about 100,000 people would have fled by the end of the year.
But that number was surpassed in July.
The agency said it was urgently trying to prepare for winter, warning that many of the refugees were still living in tents.
For much of the past 18 months rebel groups have been fighting against the regime of President Bashar al-Assad.
Activists estimate more than 27,000 people have died in the violence.
Repeated efforts by the international community to find a diplomatic solution have foundered because of a deep divide at the UN Security Council.
Late on Wednesday US Secretary of State Hillary Clinton said the Security Council was “paralyzed” and urged the members to overcome their differences.
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