Justice Secretary Liz Truss will resume talks with the prison officers' union later today amid claims the service was "in meltdown".
Up to 10,000 members of the Prison Officers Association held protests around the country on Tuesday after talks with the Government over health and safety issues broke down.
Officials were ordered back to work after the Government sought an injunction at the High Court.
On Wednesday, Ms Truss told Good Morning Britain she was "determined" to deal with the issue of health and safety in the UK's prisons.
However, she insisted she would not apologise to prison workers after appearing to suggest the union willingly walked away from the negotiating table.
"I'm very concerned about the issue of safety and violence in our prisons and I'm determined to deal with it", Ms Truss told GMB.
She added: "I'm pleased that prison officers have come back to work. I want to work constructively to improve the safety in our prisons".
Ms Truss said the government had considered retention payments for prison staff, as well as rolling out new drugs tests within prisons and implementing body-warn cameras.
The Justice Secretary said she was pleased to be re-negotiating with the POA, adding that the Government had made an initial offer around health and safety.
But she insisted she would not apologise to the union for the failed negotiation.
"They didn't come back on the offer - that was the issue", Ms Truss said.
"They did not come back on the offer, instead they instigated unlawful industrial action".
She added: "I want to make things in our prisons better. That is why, despite this, I have said that because officers have gone back to work I am willing to meet them".
Earlier this month, Ms Truss unveiled her blueprint for prison reform, which includes a recruitment drive to add 2,500 new officers to the front line and the introduction of "no-fly zones" around prisons.