Airlines in the U.S., Europe and Asia are preparing to temporarily reduce some flights and routes to inspect aircraft affected by the recall of hundreds of Pratt & Whitney jet engines, leaving the unit of the aerospace and defense company RTX facing a potential multibillion-dollar bill.

Some 137 engines used on Airbus single-aisle jets would need to be inspected over the next several weeks, RTX said Friday. That is fewer than the 200 originally expected but still a problem for carriers that were already dealing with staffing shortages and air-traffic control congestion.

The ability of RTX to contain and fix the problems has major ramifications for one of the world’s biggest aerospace and defense companies. It will also help decide whether Airbus can continue efforts to boost the production of its single-aisle jetliners. Airbus said that the engine problems won’t affect production this year, but that it will be watching for any impact after that.

Spirit Airlines said Thursday it would pull seven Airbus A320neo-family jets from service in the fall for inspection. More than 40 of Spirit’s fleet of around 200 jets are affected, and the airline said the engine problems could reduce its ability to add more flights next year.

Hawaiian Airlines said it would suspend some routes and reduce its number of flights to deal with engine inspections in the coming months. Other carriers including Germany’s Lufthansa, Mexico’s Volaris and JetBlue Airways in the U.S. have said they are evaluating whether to cut flights.

Pratt said recently that a fresh analysis following the discovery in 2021 of contaminated metal parts uncovered the need for more-immediate inspection of engines. The company said around 1,200 engines could suffer cracks faster than expected.

The company said Friday that it told customers which engines would have to be inspected over the next few weeks and which could wait to be checked over the next year.

What started as a minor quality concern escalated in recent weeks to require hundreds of engines to be removed from Airbus A320neo aircraft for inspection and possible repair. The recall adds to durability problems that have dogged Pratt since it introduced its fuel-efficient geared turbofan, or GTF, to airlines in 2016. The engines have been popular because they cut fuel consumption by around 15% and have low emissions.

RTX has sold more than 10,000 GTF engines. Compensating customers for inspections and repairs that take planes out of service could delay profitability for the program. Some analysts estimate that it will be 2030 before RTX starts to recoup its investment in the engine. It has taken an initial $500 million charge to cover the cost of new inspection, repair and compensation for the first batch of GTF engines being checked.

The company, formerly known as Raytheon Technologies, already has to pay compensation to airlines for older problems with GTF engines used on Airbus jets. These include oil-leak and vibration concerns that have required extra servicing.

With more than 100 Pratt-powered Airbus jets—around 10% of the A320neo and A220 fleet—already grounded by durability problems and spare-parts shortages that have dragged on for years, RTX Chief Executive Greg Hayes in late July embarked on a round of customer calls.

“No one is happy,” Hayes said in an interview last month.

Decades ago, Pratt engines powered the original Boeing 737s, but the manufacturer lost out to General Electric and French partner

Safran’s rival turbine for the jet and the Airbus A320 in the 1980s. That left Pratt reliant on making engines for larger jets and military aircraft, as well as propeller planes.

The introduction of the geared turbofan to airliners provided Pratt a way back to that market, using technology developed for propeller planes over the previous two decades.

Plane makers were initially reluctant to try the new type of engine as existing turbines continued to improve fuel efficiency and reliability. Canada’s Bombardier signed up for the GTF in 2007 for its new CSeries jet. The plane was designed to challenge Airbus and Boeing

in the single-aisle market.

The pivotal moment for the GTF came in 2010, when Airbus launched the A320neo, a revamped version of its A320, with the option to configure the plane with the new Pratt engine.

Airbus eventually bought control of the Bombardier CSeries program, renaming it A220 and expanding its fleet of GTF-powered planes.

Airbus sales exploded. Boeing accelerated the development of the 737 MAX, with new engines from GE and Safran, to compete with the A320neo.

The Airbus decision to launch the A320neo gave Pratt a way back to the single-aisle jetliner market. Pratt also had a first-mover advantage over GE and Safran, which produce engines through a 50/50 joint venture called CFM International.

Airbus offered both the GTF and a CFM engine called Leap for the A320neo. Boeing kept its exclusive relationship with CFM to provide only the Leap on the 737 MAX.

Both engine types have delivered better fuel efficiency and suffered from durability problems requiring frequent repairs. CFM has been quicker to resolve the concerns, helping it win a larger share of the market.

Write to Doug Cameron at Doug.Cameron@wsj.com