June 13 (Reuters) - Boeing (BA.N) delivered 50 jets in May, 13 fewer than European rival Airbus (AIR.PA), but a 43% improvement on the same month last year.

Deliveries of the cash-generating Boeing 737 MAX increased to 35 jets in May, Boeing said Tuesday. The company handed over only 17 MAXs to customers the prior month, when Boeing found a bracket installation defect that forced it to fix aircraft before delivery.

Boeing also delivered eight widebody 787 Dreamliners, three 767 freighters, three 777 freighters and a 737 that will be modified into a P-8 Poseidon maritime patrol aircraft for South Korea.

Boeing's monthly orders and deliveries snapshot comes a week before aerospace executives gather for the Paris Air Show, where both Boeing and Airbus are expected to cement new deals.

At the same time, both airplane makers are struggling with supply chain challenges that threaten to curb deliveries - a closely watched metric for Wall Street analysts, as Boeing and Airbus receive the bulk of payment for aircraft after handing over jets to customers.

Boeing has started to deliver reworked 737s, Chief Financial Officer Brian West said in late May, adding the company predicted MAX deliveries would increase from about 30 per month to about 40 per month in the second half of the year.

However, Dreamliner deliveries could slow in June due to a new production glitch disclosed by the company last week. The problem, involving miniscule gaps in a fitting on the horizontal stabilizer located at the base of the 787's tail, must be fixed before Boeing can hand over planes to customers.

Boeing booked 69 orders in May, including 59 MAXs and 10 Dreamliners. It also reported 11 cancellations, which included four 737 MAXs for Air Niugini, six 777 freighters for Hong Kong International Aviation and one 777-300ER for an unidentified customer.

Over the first five months of the year, Boeing delivered 206 aircraft - fewer than rival Airbus, which has delivered 244 over the same period. Airbus is also slightly ahead on net orders, with 144 to Boeing's 127.

Reporting by Valerie Insinna Editing by Mark Potter

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