Relations between staff representatives and the largest local authority in the UK are the "worst in the country", the GMB union claims.
Last month, about 4,000 mainly female Birmingham City Council staff won a case for equal pay. Unions estimated staff could collectively be owed £80m.
The GMB, which represents 8,000 staff at the council, said bosses should stop stalling and start negotiating payouts.
The council said the union's claims were not true, nor justified.
The authority has until 16 June to decide whether to appeal against a tribunal ruling on equal pay, made on 27 April.
The pay dispute centred on the council's old bonus structure and the tribunal ruled that bonus payments to men were discriminatory and typically allowed male employees to earn more than £50,000 a year.
Negotiations over the pay structure date back to the late 1990s.
Brian Strutton, the National Secretary of the GMB Union, told BBC News: "Industrial relations there are the worst in the country.
"I see things up and down the country and there are problems all over but I have to put them at the top of the list.
"It's down to a culmination of things. You can deal with the most difficult economic times and take the workforce with you or you can bully and not take them with you and Birmingham took the latter route.
"They've used obstructive moves, they have delayed things when they know they have got to pay this money."
In a statement, Councillor Alan Rudge, Cabinet Member for Equalities and Human Resources, said: "This statement is not true, nor is there any justification and I am disappointed by the comments.
"We have always and will continue to engage with our trades unions as we have done to date."
In February, the council said up to 2,000 jobs could be axed during the next financial year as it tried to make savings of up to £69m.
But Mr Strutton said the tribunal ruling should not mean any more job cuts as the council has "known what's coming" and had made provisions.
"If Birmingham is true to its word there will be no jobs cuts but, their track record is not one of being true to its word.
"The obvious thing to do is stop delaying and actually give their legal representatives permission to negotiate to bring these claims to an end."
'Bonus schemes removed'
Many of the staff involved in the pay claim were part time, low-paid workers, including cleaners, cooks, care assistants and caretakers, who argued they should be paid the same as their male colleagues.
After last month's tribunal ruling, Councillor Rudge said the "inappropriate bonus schemes" were removed in 2007.
Salary details released during the hearing showed some workers received thousand of pounds in bonuses and performance-related payments.
Payouts to staff following the ruling would be backdated over six years and are estimated to be about £20,000 each, the GMB said.
It represented about 1,400 people in the dispute and estimated they would receive just under £30m.
When workers represented by other unions or no-win-no-fee lawyers are included, the total compensation could amount to £80m, a GMB spokesman added.