BRUSSELS, March 19 (Reuters) - The widening conflict in the Middle East will push up airline ticket prices and leave "no winners," Willie Walsh, head of the International Air Transport Association told Reuters on the sidelines of an airline event in Brussels on Thursday.

The comments come as attacks on oil facilities in the Gulf have pushed crude prices up over $100 a barrel, rattling the aviation market, while missile and drone threats have snarled airline traffic to normally busy Middle Eastern transport hubs.

Walsh, in an exclusive interview, said that global demand remained robust for now, but that airlines were starting to shift capacity and could cut capacity if the conflict drags on and leads to shortages of jet fuel supply.