Edgar said council officials hoped to meet with Unison earlier but the union had not attended the meeting.
He added: “The offer which has been unilaterally rejected by Unison would have taken dismissals off the table and seen additional cash for those members of staff, and members of all unions, who are due back pay.
“It beggars belief that they would betray their own members in this way.”
Unison Scotland regional organiser Mandy McDowall said: “Glasgow City Council staff are not going to be bounced into a shoddy deal by bosses trying to bully them with arbitrary deadlines.
“The council’s decision to dismiss workers helps nobody and Glasgow City Council risks being labelled a pariah employer if it refuses to negotiate in good faith with its staff.”
She added Unison would continue to work to secure a fair deal and would ballot its members on an offer once discussions had finished.
Graham McNabb, an industrial officer with Unite the Union, said: “Glasgow City Council must remove direct threats to our membership in its proposed new pay and grading structure, whether it is through cuts to terms and conditions, or the scandalous threat of fire and rehire tactics.
“If they go down this reckless path then it will be met with the full force of Unite.”
