More than 4,200 Iraqis from Mosul fled to Syria in May, the United Nations refugee agency said on Friday, adding it is gearing up for up to 50,000 people to leave the Daesh-held city and cross the border. Driving the exodus appear to be reports that the Daesh militants have stepped up executions of men and boys in Falluja since Iraqi government forces launched an offensive to re-take the city, where people are also dying of starvation, the UN High Commissioner for Refugees (UNHCR) said. The Iraqi army launched an offensive on Monday to dislodge the militants from Falluja, 50 km (32 miles) west of Baghdad. Falluja was the first Iraqi city to fall under ISIS control, in January 2014, and has been under a tight siege for about six months. Iraqi forces, with help from a U.S.-led coalition, are expected to push later this year to retake Mosul, ISIS' de facto capital in Iraq. "We've seen actually a spike in the numbers of Iraqi refugees who are risking the dangerous crossing into Syria in a desperate bid. Just picture this, we have refugees fleeing to Syria. So it's a desperate bid to escape (Daesh)-held Mosul," UNHCR spokeswoman Melissa Fleming said. "The reasons for that are the pending battle to re-take it (Mosul). They, I'm sure, hear what's going on in Falluja and want to leave before they too are trapped. But also there is fighting in the surrounding areas that is driving people to leave." The 4,266 Iraqi refugees from Mosul, who walked for several days through extremist-held territory into Kurdish-held Hasaka province, "are living now in relative safety, if you can say that for Syria", in al-Hol camp about 14 kms from the Iraqi border, Fleming said. "Right now it's a bit over 4,000 but it is in anticipation of 50,000. There are contingencies for potential numbers who could be coming in ... They don't have many other options of places to flee in that region, so we're getting ready." The UNHCR has begun a five-day air lift to bring aid supplies from Jordan to Qamishly, where it will be loaded on trucks for distribution to Iraqi refugees and internally displaced Syrians.