Inflation is currently running at 2.5%. The three main local government unions - Unison, the T&G and the GMB - submitted a claim in November for a substantial flat-rate increase and a minimum wage of£4.26 an hour.
More than 100 employer and trade union representatives met at Transport House, the T&G's London headquarters, on Tuesday. Employers offered to increase the£12.5 billion combined pay bill for manual and white-collar staff in England and Wales by£250m.
They indicated they would consider distributing the extra money in different ways throughout the workforce. Unions want the pay increase to be loaded towards the lowest paid workers.
'There can be no settlement that does not defend and improve living standards and ensure action for the low paid.'
Unison head of local government Keith Sonnet said the 2% increase was rejected because there would be little for senior staff if the money was loaded towards low earners.
CIPFA chief economist Chris Trinder said the teachers' pay award has left local government staff scrabbling around for the remains.
In a phased deal, teachers will get a 3% rise in April and more later in the year. Their award was also staged last year.
'Local government staff have to some extent cross- subsidised the other groups,' said Mr Trinder. 'That's not the way to run an effective local government service.'
Manual and white-collar workers, chief officers and chief executives all settled for a 2.9% increase last year.
Employers secretary Charles Nolda said: 'Local government pay settlements over a longer period have more than matched inflation.'
The offer reflects the cost of putting manual and white-collar workers on the same pay spine.
Both sides are hoping to harmonise terms and conditions for local government workers, under a separate national deal currently being negotiated.
Negotiators will meet again on 10 March, and the settlement will be awarded from 1 April.