Opposition parties have stepped up calls for Cathy Jamieson to resign as justice minister over blunders in the privatised prison escort service.
Cathy Jamieson said she will not be resigning
The Tories joined the Scottish National Party in demanding that she quit almost two weeks after security firm Reliance let a killer walk free from court.
The calls have been rejected by Ms Jamieson, who addressed the Scottish Parliament on the issue on Wednesday.
Reliance welcomed her statement while admitting that it must do better.
Ms Jamieson told MSPs that Reliance "seriously underestimated" the challenge of implementing its prison escort service.
She said the release of convicted killer James McCormick was "inexcusable".
SNP justice spokeswoman Nicola Sturgeon said the assurances the minister had sought from Reliance amounted to "closing the cell door after the prisoner has bolted".
"It is time for Cathy to go," she said.
"Her role as minister was to ensure that Reliance were up to the job before giving them the contract not simply clear up the mess afterwards.
"She has now admitted that they weren't up to the job, they underestimated the scale of their task and responsibility for that can only lie at the door of Cathy Jamieson."
The Scottish Tories' justice spokeswoman, Annabel Goldie, backed the SNP calls.
"In my opinion she is going to have to resign because there is a huge question of public confidence in her political credibility," she said.
"We have got a convicted murderer on the loose at the moment, not recaptured. That is public safety and that is part of public confidence.
"I think her position has become untenable."
However, Ms Jamieson told BBC Radio Scotland that she would not be resigning.
"I think the responsibility on a minister is to ensure that problems are solved," she said.
"Some people in the face of problems might turn away, might walk away from them.
"I have no intention of doing that and I never did."
Tom Riall, managing director of Reliance, said the company took immediate action to review and strengthen identification procedures following McCormick's escape.
"We are grateful the minister acknowledged these improvements along with our full and sincere apologies for this incident," he said.
"We fully accept the minister's comments that the Reliance procedures for transferring prisoners into courts is more robust than the previous method, and
therefore, more time-consuming."
The company accepted that its current service was "far from error-free" and that there were inconsistencies and gaps in the way information was recorded.
Mr Riall added: "At present we have a further 55 prison custody officers under training and greater emphasis will now be placed on court procedures as well as more emphasis on security."