The motion, which proposed treating all trans women the same as cisgender women, passed unanimously on Wednesday.
Joe Anderson told the council meeting Liverpool ReSisters proposed hate “against people that are different”.
The group’s spokeswoman had told councillors the motion weakened “both safeguarding and equality frameworks”.
The motion also included a commitment to light council buildings in the “transgender colours of blue, pink and white” and fly the “transgender flag” at the town hall for one weekend a year.
It also encourages developers to include gender neutral toilets in their plans.
Transgender : Applies to a person whose gender is different from their “assigned” sex at birth
Cisgender : Applies to someone whose gender matches their “assigned” sex at birth (ie someone who is not transgender)
Non-binary : Applies to a person who does not identify as “male” or “female”
Genderfluid : Applies to a person whose gender identity changes over time
See also: A guide to transgender terms
The Liverpool ReSisters’ spokeswoman said the group were concerned about self identification, a process by which trans men and women self-declare the gender in which they choose to live without the need for medical evidence or proof.
“Self ID erodes vital safeguarding principles by preventing women and children from listening to their feelings of discomfort,” she told the council chamber.
“I urge the council to… listen with an open mind to all sides of the issue [and to] consider the complexity of self ID and the full impact its implementation will have on Liverpool citizens.”
In an angry response, which the Local Democracy Reporting Service said received a standing ovation, Mayor Anderson said the council had “united against the behaviour of the ReSisters in defacing public art in what I believe to be, and I am proud to state, that was done in a hateful way”.
The group put stickers on a statue on Crosby Beach in Sefton, an action which is being investigated by Merseyside Police as a possible hate crime.
The mayor said the campaign had resulted in “torrent of abuse” being directed at “transgender groups… myself and other councillors”.
He said their behaviour was not about “having an open debate, it’s about bullying, it’s about intimidation and it’s about proposing hate against people that are different and that’s something that every single person in this council rejects”.
“If you approached it in a different way and wanted to have a sensible discussion with us then we would have listened,” he added.
“But we won’t tolerate abuse of members of this community that we respect, value and love.”
Lesbian, gay, bisexual and transgender rights group Stonewall said the motion “sends a very powerful and very welcome message of acceptance”.
“Not only has the council reaffirmed its commitment to trans inclusion and equality, it’s gone a step further with plans to host a public, visible celebration of trans equality in the city centre.
“The bullying and abuse of trans people is at epidemic levels [and] to change this we need to see more visible support and leadership from organisations and institutions across Britain.”