Labour leader Warren Morgan has turned on GMB members and criticised them for industrial action.
Councillor Morgan said: “Residents will have run out of patience on this and we do not see that further action is justified in light of the offer from the council.
“We urge those taking action to think again and return to work, so that people across the city who have no part in this dispute can once again have their bins collected.”
Conservatives welcomed Cllr Morgan’s new stance – as all sides apologised for the continual disruption.
Mark Turner, of the GMB, which represents truck drivers at the centre of the dispute, said: “We have had a number of discussions with council officers which culminated in a proposal they put forward to attempt to avert current action.
“Unfortunately, our members rejected this because the timeframes that were set by the council weren’t considered reasonable and they still have little confidence that management would meaningfully look at their job description and take into account the professional element of their driving licence.
“We have informed the council today of the position, but have clearly stated that we are willing to continue discussions to attempt to resolve the situation
“We can only apologise again for the effect this has on the public, but this is not of our members’ making and we have been trying to resolve this for a considerable number of weeks before taking any industrial action.”
Geoff Raw, Brighton and Hove City Council’s executive director for environment, development and housing, said: “I am really disappointed that we have been unable to reach an agreement with the GMB and deeply sorry that we are likely to face more industrial action.
“We did agree with the GMB that we will work together on a full service redesign, but we are unable to raise the salaries of one group of workers without equal pay implications across the entire organisation. Please be assured we are working to do all that is necessary to develop a service which meets the city’s needs.”
A service update on the council website last night said: "All crews have been out on their scheduled rounds today, including the communal refuse and recycling crews, There are also two spare crews out collecting refuse, who will be focussing on the Preston Park area and Hanover.
"During the industrial action we are limited in our ability to provide additional resources to catch up any missed collections as the drivers continue to 'work to rule'. If your collection has been missed please leave your containers out and we will catch up when we can. Again, we apologise for the ongoing service disruption."
The strike is part of an ongoing row over pay and conditions that has been ongoing for almost five years.
It was sparked by a reorganisation of pay and conditions throughout the council to ensure similarly-skilled people doing roles traditionally carried out by either men or women are paid the same.
CityClean workers are also working to rule, which means a ban on overtime and no picking up rubbish not placed in bins or recycling boxes.
The strike follows months of unreliable collections, often due to trucks breaking down, which means rubbish was already piling up on the city’s streets.