LE BOURGET, France—Airbus and Boeing exit the Paris Air Show with more than $107 billion in deals and slightly fewer orders than at the industry’s showcase gathering of recent years, though still enough to sustain pressure on the plane makers and their suppliers to build more jets.

Airbus Group SE beat rival Boeing Co. with $57 billion of sales agreements for 421 planes against the Chicago-based plane maker’s intake of 331 jets valued at $50.2 billion. Two years ago, the industry booked more than $134 billion in deals here. Last year, it recorded $115.5 billion, for almost 700 jets, at the Farnborough International Air Show, which alternates with Paris.

Airbus secured a last-minute deal Thursday for 110 A320neo single-aisle jets from Central European discount carrier Wizz Air before its closing news conference. That allowed it to defend its home turf and best Boeing for the bragging rights of taking in the most commitments for new planes.

Both aircraft makers have said the record pace of order bookings of years past would start to moderate because bulging backlogs of jets mean many airlines have to wait years to get new ones, hampering their appetite to buy more. The strong U.S. dollar also is an impediment to sales to airlines based in other markets, executives said.

Still, this week’s sales activity “is higher than I personally expected,” said Fabrice Brégier, chief executive of Airbus’s plane-making unit as he confirmed the company remained on track to book more firm orders this year than the roughly 630 jets it will deliver.

The order tally bolsters the case to increase production output of some of the most popular planes, he said. Airbus might decide this year whether to lift production levels for its popular A320 single-aisle jet underpinned even more by the 366 narrow-body commitments garnered this week, he said.

That is a sentiment echoed by Boeing Commercial Airplanes Chief Executive Ray Conner. Mr. Conner said demand for jets outpaces supply, adding pressure to push output even higher.

Unlike car makers, though, the aircraft industry isn’t used to mass production, and the need to build more planes is starting to test the limits of what some suppliers to plane manufacturers can handle.

Turboprop maker ATR, the joint venture of Airbus and Finmeccanica SpA is holding off on raising output because others lift production plans.

“With the ramp-up [of production] at Airbus and Boeing, and Dassault as well, the supply chain is very much under pressure,” ATR Chief Executive Patrick de Castelbajac said.

Executives for CFM International, whose engine powers all Boeing 737 single-aisle jets and about half of A320 planes, on the eve of the air show warned plane makers not to ask to build more planes than planned before 2020. The engine joint venture between General Electric Co. and Safran SA is facing its steepest-ever industrial ramp-up and is stretched to capacity building what has already been ordered, they said.

That isn’t a message that Airbus wants to hear. “If one engine manufacturer didn’t want to follow us increasing production that would be very disappointing,” said Airbus’s chief operating officer for customers, John Leahy.

Airbus is even having second thoughts about a production cut it announced this year to its A330 wide-body as demand softened during the transition from the current version to an updated model due in 2017. Production is set to go to six planes a month next year from 10 today. That might be too much, said Mr. Brégier. “If we can deliver a couple of aircraft on top of that we will not hesitate,” he said.

Boeing is trying to avoid the same path as Airbus. The plane maker won orders for nine current-generation 777 jetliners. The long-range jet is the company’s cash cow and Boeing is hoping to avoid cutting output from about 100 each year, as it transitions to a heavily updated model in 2020.

Boeing also used the air show to bolster one of its weakest programs, the 747-8 jumbo jet. The plane maker later this year will reduce its output to an average of 1.3 planes a month, or about 15 to 16 each year, down from 1.5 monthly. Russia cargo operator Volga-Dnepr Group’s commitment for 20 more of the planes could bridge a gap to future orders from other customers, said Randy Tinseth, Boeing commercial airplanes marketing vice president.

For suppliers, the message leaving Paris was a clear one: Pressure is mounting. Tony Wood, president of Rolls-Royce Holding PLC’s aircraft-engine unit said: “This air show is not about new [aircraft]. It is not about big new orders because we are booked out to 2021. It is really about ramp-up.”