In its latest briefing on the Syria crisis, the UN refugee agency also said 250,000 people were living in temporary shelters in the flashpoint city of Homs, without adequate food, clothing or medicine as winter added to the misery of civil war.
"We have received very disturbing reports from Syrian refugees in Jordan who say they were targeted as they were fleeing. UNHCR calls on all sides to ensure that at least civilians have access to safe passage outside the country," spokeswoman Melissa Fleming told a news briefing in Geneva.
It was not clear who was taking aim at civilians as they ran for their lives under cover of darkness.
"These reports are generally kept highly confidential, people are terrified. They don't like having their stories told," Fleming said.
Some families sedate their children during the journey to the border to keep them "calm and quiet", Fleming said.
More than 465,000 Syrians have registered as refugees in neighboring countries and North Africa. Thousands more have not signed up for refugee status and assistance, the UNHCR says.
Nearly 138,000 are registered in Jordan, where the largest camp at Zaatri north of Amman houses more than 32,000.Grim conditions in Homs
A UNHCR team managed to reach Homs this week, where they found 250,000 displaced people living in "squalid" conditions in the city of 1 million, Fleming said.
"They saw thousands of displaced people living in unheated communal shelters. They also observed that half of the city's hospitals are not functional and there were severe shortages of basic supplies ranging from medicine to blankets, winter clothes and even children's shoes," she said.
One communal building sheltered 70 families, or 400 people, while at another "2,300 people are crammed into an abandoned public building, the largest such shelter in Homs".
"These are displaced people, some may be from Homs and left their embattled neighborhoods as their homes were destroyed, others come from other parts of the country and have been displaced many times," Fleming said.
Some city hospitals have been converted into communal shelters and 60 percent of Homs doctors have left, along with other medical personnel, according to the agency.
A UNHCR convoy of nine trucks delivered winter assistance to Homs during the two-day visit ending on Thursday night, including quilts, sleeping mats, winter blankets, mattresses and sanitary napkins.
"We are scheduled to deliver more aid in coming days. We have a better idea of needs in a city going through tremendous shelling since the beginning of the conflict and is really in a desperate situation," Fleming said.
GENEVA (Reuters) -- Syrian refugees are being shot at as they flee to neighboring Jordan and many have to be treated in hospital on arrival, the United Nations said on Friday.