The newspaper has been widely boycotted in the city because of its accusations following the Hillsborough disaster.
A motion put forward at a meeting on Wednesday night condemned the paper for its "blatant lies" about the tragedy, in which Liverpool 96 fans were killed.
The Society of Editors said the council was "stretching towards censorship".
Put forward by Labour councillor Mary Rasmussen at Liverpool Town Hall, the motion said: "Due to crowd control mismanagement those fans, whose ages ranged from 10 to 67 years old, had the life crushed out of them.
"Contrary to the facts, The S*n published a front page story with the banner headline 'The Truth' which contained blatant lies.
"For this reason we call on all retailers and vendors of newspapers in Liverpool to stop selling The S*n," said the motion, which recognised the efforts of the campaign group Total Eclipse of the S*n to "rid" the city of the newspaper.
The Sun said it had no comment on the vote, although the newspaper and the editor at the time of the Hillsborough tragedy have previously apologised for the coverage.
Relatives of Hillsborough victims attended the full council meeting, where mayor of Liverpool Joe Anderson said the newspaper would "never, ever be forgiven", and if he could legally do so he "would ban it from shops across the city".
However, Bob Satchwell, from the Society of Editors, which represents about 400 media outlets, said: "In a free society people must be free to choose which newspapers they read or sell.
"The comments from Joe Anderson demonstrate the danger when he says that if he has his way he would ban The Sun. That is what happens in dictatorships and banana republics."
Everton-based newsagent Ronald Butterfield also said it was "wrong for the council to get involved".
"I don't sell it but it is up to people to decide."
He added: "When I tell people who aren't from Liverpool I don't sell it they look at me like I've got knickers on my head.
"One Liverpool man who always bought it for the horses not the news cancelled it because he was worried about the paperboy being seen delivering it."
Explaining why a council-backed campaign was necessary in a city where The Sun is widely boycotted, Emily Heywood of the Total Eclipse of the S*n group said that with new newsagents and changing owners some retailers "had started selling it again and it wasn't being questioned".
All 96 fans who died as a result of a crush at Hillsborough were unlawfully killed, their inquests concluded in April.
A campaign calling on retailers in Liverpool to stop selling The Sun has received the unanimous backing of city councillors.