Social media criticism "sent in a tone of assault" can make councillors' lives a misery, according to a Central Bedfordshire Council executive member.
The local authority wants to provide clearer guidance to councillors over use of social media.
It can advise residents of work being done and help obtain useful information from them, according to a report to the council's general purposes committee.
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Conservative Stotfold and Langford councillor Steve Dixon warned: "We need to find an integral form of challenge and not attack, because challenge is healthy, attack isn't.
"I think all of us here have been subjected to social media given and sent in a tone of assault.
"That's what makes some councillors lives a misery. We can't endorse that. It has to be challenged.
"Consequences needs to be included in this. There was once a filter called a newspaper.
"There's no filter any more. People say what they want," added councillor Dixon, who's the executive member for sustainability and transformation. I don't think this ever rests. It's the beginning not the end."
CBC deputy leader and Conservative Cranfield and Marston Moretaine councillor Sue Clark said: "The Local Government Association (LGA) has been doing a lot of work on the councillors' code of conduct.
"It applies to all forms of communications and interactions, including electronic and social media posts, statements and comments, and interactions with the public, councillors and local authority officers.
"I propose this policy is reviewed immediately in line with the LGA code and a revised draft brought to the committee."
CBC proposed the social media protocol for councillors be approved, included in the constitution and made public on its website, said the report.
Independent Toddington councillor Silvia Collins said: "We need more teeth to this and to be encouraging very high standards of behaviour within our council, and we need consequences of breach.
"We've got an opportunity by taking into account this councillors' code of conduct guidance coming out of the LGA."
Liberal Democrat Houghton Hall councillor Yvonne Farrell told the committee: "I wonder if it's robust enough to protect councillors, as well as the reputation of the council.
"Could it be revisited soon to include protection for councillors from social media abuse which impacts on health and wellbeing?" she asked.
"Also guidance on how to approach cruel allegations made by the public about them or any other councillor."
Independent Linslade councillor Victoria Harvey described her shock over public comments that being a councillor is all about attacking each other and they would never want to do the role themselves because of the abuse.
"I thought that's terrible if residents see the work we do in that respect," she explained. "We risk losing really good people and officers to this council if it's somehow seen as awful.
"What we need desperately nationally is how we have respectful debate and how we properly challenge, criticise and scrutinise while showing respect."
Conservative Leighton Buzzard South councillor Amanda Dodwell said: "People can unwittingly say and print things online that if they thought about it they'd never say to anyone in a meeting.
"It's a bit like the wild west out there. People think they can get away behind their keyboard and put all this out there without really thinking about the consequences.
"If you're an elected member you have a sense of responsibility to ensure your comments don't incite unrest or cause offence.
"It's fair enough to have a lively debate over the issues. We all want that. But we don't want one that's disrespectful."
The committee agreed councillor Clark's suggestion to approve the social media protocol for councillors and review it in light of the LGA guidance.