Safran co-owns the world's largest jet engine supplier, based on the number of units produced, along with General Electric and their plans for a record hike in output of LEAP are 4-6 weeks behind schedule.
"I want to be virtually certain about the robustness of the supply chain before committing to higher production," Philippe Petitcolin said.
CFM International, the joint venture that makes LEAP engines, aims to deliver around 1,100 of the engines this year, followed by 1,800 next year and hitting the 2,000 mark in 2020.
Its factories are currently churning out 12 LEAP engines a week for the Airbus A320 family and 14 a week for the Boeing 737. By the end of the year it aims to raise the weekly rate by two engines for Airbus and 4-6 for Boeing, Petitcolin said.
Engine makers have been struggling to keep up with demand triggered by a new generation of fuel-saving engines.
CFM has been spared most of the delays felt by rival Pratt & Whitney or technical problems seen at Rolls-Royce, but its performance has widespread economic implications since it powers 75 percent of the world's most-used narrowbody jets.
Petitcolin said CFM continues to see demand for the previous generation of engines, its decades-old CFM56, even as it switches to the new fuel-saving model. Analysts say airlines calculate that current engines are still economic on shorter trips.
Safran is juggling the LEAP ramp-up against efforts to turn around French aircraft seats and cabin equipment maker Zodiac Aerospace, which Petitcolin said occupies much of his attention.
Three months after taking control of Zodiac, Safran has not discovered any nasty surprises - seen as a significant fact in its own right after around 10 profit warnings from Zodiac beforehand.
"There have been no major (bad) surprises but there haven't been any good surprises either," Petitcolin told the AJPAE aerospace media association, adding it would take 12-18 months for delayed airline seat projects currently being handled by Zodiac to work their way through the system.
Petitcolin deflected questions about intermittent speculation in France of a future tie-up between Safran and French defence and aerospace equipment company Thales.
The two companies faced pressure to merge more than a decade ago but never went through with a deal. Thales later fell into the orbit of Dassault Aviation, which has industrial control as part of a shareholder pact with the French state.
Industry sources say the mosaic of state-influenced French aerospace companies could again come under scrutiny following the death this week of industrialist Serge Dassault.
In 2012, one of his sons, Laurent Dassault, suggested a broad combination of Dassault Aviation, Thales, Safran and Zodiac as a counterweight to Franco-German Airbus group (then called EADS), but few in the industry publicly warmed to the idea.
Petitcolin paid tribute to Serge Dassault as a "great man" of French aeronautics, but declined to be drawn on any future industry deals, saying his priority was to integrate Zodiac.
Safran meanwhile hopes for an inaugural contract for its new E-Taxi electrically powered aircraft taxiing system at the Farnborough Airshow in July, Petitcolin said.
(Reporting by Tim Hepher; Editing by Richard Lough and Susan Fenton)
By Tim Hepher