"The construction will continue right to the end," Ayrault said on RTL radio on Thursday.
"There are difficulties but I think we have to accept that because it is necessary."
French energy group EDF on Monday raised the total cost of its long-delayed new-generation nuclear reactor at Flamanville in western France by 2 billion
euros ($2.6 billion) to 8.5 billion euros.
The cost of the facility, slated to begin operations in 2016, is now 5 billion euros more than initially estimated.
Built by Areva and due to be operated by EDF, Flamanville is one of four European Pressurised Reactor projects in the world, including another much-delayed one planned in Finland, whose production date has been delayed indefinitely.
Two other EPR reactors are being built in Taishan in southeastern China.
Ayrault said that as Flamanville is one of the first EPR reactors to be built additional precautions have needed to be taken and the delays have been
pushing up the cost.
He noted that safety standards are now higher and that the reactor was being designed to last 60 years, which also implied higher construction costs.
Ayrault also noted that the reactor had its opponents, including from the Greens inside the Socialist-led government, but said "this reactor will be the
safest in the world."