International Airlines Group saw traffic rise by 3.4% last month over April 2017.
The owner of British Airways, Aer Lingus, Iberia, Vueling and Level increased capacity in the month by 4.9%.
However, the passenger load factor at BA fell by 1.9 percentage points to 81% year-on-year.
IAG’s main growth came from domestic routes in the UK, Spain, Ireland and Italy, which rose by 9.8%.
Overall passenger numbers rose to 9.1 million in the month, giving a year to date total up 7.3% to 32.1 million.
Carryings to Africa, Middle East and South Asia fell by 3.1% year-on-year and in the Asia Pacific region by 1.1%.
This was countered by 3.2% growth in Europe, 3.8% on North American routes and 4.4% to Latin America and the Caribbean.
BA and Iberia last month introduced ‘basic’ long-haul fares, excluding checking in bags and seat selection.