Trade unions have pushed back after being urged to accept a 'final' 2.75% pay increase for council staff.
The National Employers called on the unions to accept their offer, which would increase the national pay bill by more than £500m.
They have also offered council employees an extra day's annual leave, taking the minimum entitlement to 22 days per year.
However, the three local government unions said the Local Government Association's (LGA) offer fell 'well short' of their 10% claim for this year and it failed to recognise the 'hard work of local government staff in keeping services running while the country is in lockdown'.
The unions have asked to write jointly with the LGA to the Government calling on it to fund an additional pay increase.
A letter from the unions to the employers read: 'We suggest that we give them a deadline of two weeks in which to respond, during which we will continue to engage with you to seek further improvements.
'Local government and school staff are working above and beyond their jobs, putting themselves daily at risk from the coronavirus to keep public services working and our country on track.
'The Government should recognise this and fund a substantial additional increase for these committed workers, who have seen their pay drop in real terms by over 20% in recent years.'
Unite national officer for local government, Jim Kennedy, said: 'This is a totally unrealistic offer, especially given the current crisis where it is our frontline local authority workers who are protecting our communities and vital services, caring for our young and our vulnerable elderly, collecting our rubbish, cleaning our streets, and working in our crematoria to ensure dignity for those who have, sadly, fallen victim to this terrible virus.
'Unfortunately, the local government employers are not mirroring public opinion with this low offer, seemingly oblivious to their many years of cynically undervaluing some of the public sector's lowest paid workers.'
Unison's head of local government, Jon Richards, told The MJ the local government workforce was 'highly underpaid'.
He added: 'The LGA says they'd like to give council staff more but it's all cash-strapped local authorities can afford.
'Although an increase on its previous offer of 2%, it still falls well short of what's both needed and deserved.'
The employers' original offer of 2% was rejected by the trade unions, which branded the figure 'deeply disappointing'.
Unions have been campaigning for a 10% pay increase.
