GENEVA — The United Nations appealed Wednesday for $1.5 billion in new aid to handle the steadily worsening humanitarian crisis created by violence in Syria and predicted that the number of refugees fleeing the conflict would double to more than 1 million in the next six months.

The increased estimate was at least the fourth time the United Nations had revised its projections upward on refugees in the nearly two-year-old uprising against the Syrian president, Bashar Assad, which has turned into a civil war that has left at least 40,000 people dead and has threatened to destabilize the Middle East.