Airbus, in a lull before the event when it traditionally makes a slew of customer announcements, added just seven orders in May, taking its gross total for the year so far to 176, behind Boeing's 182.
After cancellations, Airbus had 97 net aircraft orders in January through May, compared with 133 at Boeing.
Airbus head Tom Enders predicted last month that the planemaker would have a larger order haul at the coming show at Le Bourget than at last year's event, held at Farnborough in southern England.
Leasing companies were top buyers at the UK show as demand recovered from the recession, helping Airbus bag 130 firm orders and 122 provisional orders.
Enders said on May 24 that a few more orders could be expected at Le Bourget, which runs from June 20-26, and that the market is active.
Airbus has unveiled a revamped version of its key A320 family of short and medium-haul aircraft in an effort to trump Boeing in the single-aisle market, the most active.
(Editing by David Holmes)