(Recasts to lead with U.N. figures) * UNHCR reports surge in perilous migration * People-smuggling flourishing in Mediterranean * Libyan turmoil exacerbates problem By Robert Evans GENEVA, Aug 26 (Reuters) - Nearly 2,000 people fleeing Africa and the Middle East have drowned in the Mediterranean this year, most of them in the past three months as they tried to reach Europe from Libya, the United Nations refugee agency said on Tuesday. "In all, we believe that 1,889 people have perished this year while making such journeys, 1,600 of them since the start of June," UNHCR spokeswoman Melissa Fleming told a news briefing. Earlier on Tuesday, the Italian navy said it had rescued 364 would-be migrants in a two-day effort after their crowded fishing boat sank off Libya. Violent political turmoil in Libya - which has long been a major departure point for people trying to reach Europe by sea - has exacerbated the problem, the Geneva-based agency said.