More than 38,000 people appealed to the United Nations for help after facing sexual assault or other gender-based violence in Syria in 2013.
U.N. humanitarian agencies have previously declined to produce statistics from Syria on gender-based violence, which covers any violence where gender is an issue, including rape, domestic violence, harassment and psychological abuse.
But the U.N. Population Fund (UNFPA) released figures this week showing it provided psychological first aid or support for such violence to 33,430 people in Syria in the first 11 months of 2013, and to another 4,800 in December in Idlib, Homs, Damascus and rural Damascus.
In Lebanon, home to the largest number of Syrian refugees at 850,000 people, the U.N. agency said it had "provided post-rape treatment to 17 hospitals and primary health care centres covering the potential needs of 1,020 survivors".
In Jordan, which hosts the Za'atari camp which houses about 85,000 refugees, about 75 "survivors" of gender-based violence access UNFPA services every month, the agency said.
UNFPA Syria Regional Response Advisor Dan Baker said it was impossible to know how the numbers in Syria compared to the pre-conflict situation, and that they did not prove that rape was being used as a systematic weapon of war.
Data is hard to collect because victims are often too scared or ashamed to seek help, so any figures are widely assumed to be a small sample of a bigger problem.
Zainab Hawa Bangura, the U.N. Special Representative on Sexual Violence in Conflict, has previously said that pro-government forces are "credibly suspected" of being responsible for patterns of rape and sexual violence.
La Niece Collins, a spokeswoman in Bangura's office, said fear of sexual violence had been one of the main drivers of the refugee exodus in the first two years of the conflict.
Rape was considered so shameful that some girls have been killed by their families in honour killings, Collins said.
"So it's really very hard to get at. But even with the numbers that we have, the testimonies that have been taken, the information that we has been gathered, we really feel that this is just the tip of the iceberg, even with just the thousands of reports, and these are just the verified numbers," she said.
Baker said anecdotal evidence suggested that domestic violence was worsening, particularly among the 6.5 million displaced Syrians living in temporary shelters and the 2.3 million refugees in neighbouring countries.
Many fathers appear to be rushing marry off their young daughters when they become refugees, Baker said.
"They feel that if they can get somebody, especially an older man who can protect them, then they've fulfilled their responsibility and the young girl or the young woman will be more protected," he said.
But many of the men marrying women in such situations were actually trafficking them into sexual slavery, Collins said.
"There is a nexus between sexual violence in conflict and organised and transnational crime," she said.