Governments are being urged by airlines to minimise costly airspace closures.
The demand from Iata came in the wake of political tensions in Iran which forced the banning of commercial flights over parts of the country last month.
At least eight major airlines cancelled or re-routed flights away from Iran after a US drone was shot down in the Strait of Hormuz.
Latest Iata figures show a “solid” 4.5% rise in passenger demand year-on-year in May, up from 4.4% in April and 3.1% in March.
However, it remained below the 20-year average growth rate of around 5.5%.
Capacity climbed by a modest 2.7% and load factor rose 1.4 percentage points to 81.5%, surpassing last year’s record load factor of 80.1%.
Iata director general and CEO Alexandre de Juniac said: “Passenger demand growth has slowed compared to the past two years. This is in line with slumping global trade, rising trade tensions and weakening business confidence.
“In this challenging environment, airlines are managing capacity carefully in order to optimize efficiency.
“Aviation is the business of freedom, connecting people and trade and creating new opportunities for growth and development. But to be effective, the business of freedom relies on borders that are open to the movement of people and goods – and aircraft.
“In recent weeks, we have seen extensive airspace closures owing to political tensions. These closures have contributed to longer and less efficient routings, higher operating costs and increased carbon emissions.
“Without any compromise on safety, it is vital that governments work to minimise airspace closures so that the Business of Freedom can continue to deliver its benefits as efficiently as possible.”