But French President Emmanuel Macron said his justice minister Nicole Belloubet, who has been negotiating with union leaders this week to end France's worst prison blockade in 25 years, had his full support.
"The minister is taking action and I'm certain she will reach a negotiated solution", Macron said Thursday.
Belloubet told union chiefs that 1,500 maximum security cells would be built, and that dangerous inmates would be handcuffed and once again subject to spot cell searches.
She also pledged to create 1,100 new jobs to ease the pressure on the 28,000 guards at overcrowded prisons, and at least 30 million euros ($37 million) to increase salaries.
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Belloubet told Europe 1 radio on Friday that they were "very serious offers" while calling for "a sense of responsibility, an appreciation of the situation."
She is expected to be auditioned soon by a Senate panel on the blockades.
France's prisons administration said 116 of the country's 188 jails wereaffected by the protests Thursday, with guards at 42 facilities refusing to show up for all or part of their shifts.
Only about 60 prisons were experiencing work stoppages early Friday.
Guards are wary of escalating their protests with threats to "lay down their keys", since they are banned from striking under French law.
But at the Fresnes prison outside Paris, one of the country's biggest, only about 20 of the 150 guards had shown up Friday, the Force Ouvriere union said.
Tensions mounted this week after the prisons administration warned that guards repeatedly calling in sick as a way of halting operations could be disciplined.
'Fearing for their lives'
Force Ouvriere and the CGT dismissed the government's offer, with the CGT saying "the essential isn't there."
Many guards now insist that they should be ranked higher in France's civil service categories, which would bolster their base pay.
Jean-Francois Forget, head of the UFAP-UNSA, the largest union for guards, said members would continue the protest Friday, although he welcomed the justice minister's "improvements".
"We've gone from 30 million euros to 34 million, and we've got 40 million euros to create new jobs," he said after Thursday's meeting.
Conditions in French prisons have long been a source of anger among prisoners and guards and an embarrassment for the state, with Macron once describing them as "disgraceful".
Adding to the guards' grievances is the radicalisation of inmates who come under the sway of jailed Islamist extremists and jihadists.
French prisons have developed a reputation for being hotbeds of radical Islam that have turned out some of the jihadists behind a series of bloody attacks in recent years.
The protests began after a convicted Al-Qaeda extremist attacked guards in a high-security facility in the north of the country on January 11 with a razor blade and scissors, injuring three of them.
A series of other assaults occurred shortly afterwards, often by radicalised inmates.
"These people go to work every day, civil servants, fearing for their security or their lives. We need solutions which respond to this concern for working in safety," Laurent Berger, head of the national CFDT union, which does not have a chapter for prison guards, said Friday.