Varin, speaking in interviews with French daily Liberation and RTL radio on Friday, also sought to ease tensions with unions by signaling flexibility over the plan's implementation.
"We would like to see a reduction of the charges weighing on labor costs," the chief executive said in his newspaper interview.
The French government is set to unveil a broad auto-sector support plan on July 25.
Shares in Peugeot were down 7.5 percent at 0915 GMT as investors reviewed the stock in the light of financial disclosures accompanying the restructuring announcement.
"The bad news is the level of pain that Peugeot are currently suffering to get to this point," Barclays Capital analyst Kristina Church said in a note on Friday, cutting the bank's target price on the shares to 5 euros from 8.5.
Announcing the job cuts on Thursday, Europe's No.2 automaker warned of a first-half net loss and said its core manufacturing division was burning 200 million euros ($245 million) a month. Operating cash flow will stay negative until 2015, the company said.
Peugeot will seek to create 1,500 new jobs through the conversion of its Aulnay factory site near Paris to accommodate other industries and companies after its 2014 closure, Varin said on Friday.
"There is room for maneuver in the implementation of these decisions," he also said.
France's new Socialist President Francois Hollande told ministers he was "extremely concerned" about the cutbacks and urged them to minimize the social fallout, his office said on Thursday.
But the government has stopped short of demanding that Peugeot abandon the plan, drawing the wrath of the country's powerful unions.
(Additional reporting by Nicholas Vinocur; Writing by Laurence Frost; Editing by Mark Potter)
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