"These are people that haven't fled the city as they haven't had the means or feel it is too dangerous to make that journey and we are getting indications that the journey is fraught with armed gangs and road blocks blocking the way," she said.
About 7,000 have taken refuge in university dormitories and many more are camped out in 32 schools, each housing 250-350 people, Fleming told a news conference. Her figures suggest a Total of 15,000 to 18,000 displaced within Aleppo.
Fighting has raged in the city of 2.5 million for a week. Helicopters fired heavy machineguns at eastern districts on Tuesday, a Reuters reporter in Aleppo said.
U.N. humanitarian chief Valerie Amos said on Sunday about 200,000 people had fled Aleppo and surrounding areas over the weekend, citing an estimate from the Syrian Arab Red Crescent.
But that has not produced a flood of refugees into nearby Turkey, about 50 km (30 miles) from Aleppo, with only 2,000 crossing the border in the past four days, the UNHCR said.
"Many report difficulties along the route, including snipers and road blocks, which may be hindering others from making the journey," the agency said.
Thousands of Iraqi refugees in Syria are heading home to escape the violence now convulsing the country where they found sanctuary following the U.S.-led invasion in 2003. The UNHCR said 20,000 had returned to Iraq in the past 10 days.
Many of the Iraqis left from Aleppo, according to the International Organisation for Migration, which said more than 2,800 Syrians had also sought refuge in Iraq, a journey that returnees say costs about $300 by taxi or $100 by bus.
Iraq now hosts more than 12,000 Syrian refugees, far fewer than the more than 30,000 registered in each of Lebanon and Jordan, and more than 44,000 in Turkey, part of an overall total of 129,000 Syrians who have registered with UNHCR.
The total number of Syrians who have quit the country is far higher, with an estimated 150,000 in Jordan alone. The IOM is expanding Jordan's Zaatari camp, which can hold 5,000 refugees to enable it to take 150,000, in case of a mass exodus.
Between 10,000 and 25,000 Syrians have fled to Algeria, where they do not require visas, Fleming said, citing information from the Algerian government. But on 70 of them have contacted the UNHCR in the North African country.
A UN official said most of those in Algeria were from Damascus and, with flights out of Syria becoming rarer, many had flown from Beirut or Amman after crossing the border.
The UNHCR has registered another 1,305 Syrian refugees in Egypt and 400 in Morocco.
UN agencies bracing for an exodus from Syria doubled the size of their humanitarian aid plan a month ago to cater for 185,000 refugees by the end of 2012.