CAIRO — When Hazem learned last month that the Syrian military would draft him on New Year’s Day, he did not wait around to see whether the regime would keep its word. The 23-year-old law student from Damascus drove to the Lebanese border, bribed a soldier and hopped on one of the next planes from Beirut to Cairo. In doing so, he joined tens of thousands of his compatriots — including his brother, who had previously fled conscription — who have fled the fighting at home for countries increasingly far from Syria.

The vast majority of the 576,000 Syrian refugees registered or awaiting appointments with the UN’s refugee agency are concentrated in nations bordering Syria — particularly Jordan, Turkey and Lebanon — but thousands more are seeking refuge in Egypt and other North African countries. Across the region, thousands remain unregistered.

Over 99,000 Syrians were living in Egypt at the end of November, when data was most recently available, up from 56,000 in August, according to an Egyptian foreign-ministry official. While Syrians have long come to Egypt to study or work, far more than usual have arrived here as a direct result of the Syrian conflict, according to the official, who requested anonymity per ministry practices.

The Office of the United Nations High Commissioner for Refugees (UNHCR) last month for the first time included Egypt in its regional response plan for the Syrian refugee crisis since the number of Syrian refugees here has “grown significantly over the past year.” Syrians here say the population is likely tens of thousands larger than the government’s number.