A university atheist society which sparked a global debate over the publication of a cartoon depicting Jesus and Muhammad on a webpage has declared a victory for freedom of speech after its student union backed away from a demand that the cartoon be removed.

The University College London's Atheist, Secularist and Humanist society garnered high-profile support from the secularist Richard Dawkins after it refused the student union's request to remove an image of Jesus and Muhammad sharing a pint from a Facebook page advertising a social event.

A spokesman for University College London's student union said the request to remove the cartoon remained in place, but that decisions regarding advertising for events remained at the discretion of individual societies. "Society presidents take responsibility for their own publicity, and it is not vetted by UCLU prior to distribution," the union said. "They are provided with equality training prior to running a society, to help them understand the balance between freedom of expression and cultural sensitivity."

But the atheist society took the move as a climbdown and thanked the thousands of secularists who signed a petition in its support.

In a statement on its Facebook page, the society's president, Robbie Yellon said: "University College London Union has recognised that mistakes were made and that the initial correspondence with our society was flawed. The union is to review its stance on such matters and has said that this will not happen again. They can no longer call on us to withdraw the image. We welcome these developments, which set an important precedent for other universities. We also feel it appropriate to recognise the swift response of the union, which certainly helped us reach this positive conclusion."

A spokesman for the students union said that the atheist society had agreed to show more consideration about how it advertised social events, but because of the union's procedure the society could still face disciplinary action.

"If people continue to complain then we are going to follow normal procedure," said James Skuse, the union's democracy and communications officer.

He said disciplinary action, which could entail forced resignation of committee members, or disaffiliation from the union, was "one possibility out of many".

The atheist society used the title page from a comic book, Jesus and Mo, by a pseudonymous British cartoonist called Mohammed Jones, on Facebook last week.

Following complaints from students it was advised by the union on Tuesday that it would be "prudent" to take the cartoon down. The society refused, launching an online petition to "defend freedom of expression at University College London" and criticising "attempts to censor" the society.

By Thursday morning the petition had nearly 3,000 signatures, including that of Richard Dawkins, who left a comment stating: "Jesus and Mo cartoons are wonderfully funny and true. They could offend only those actively seeking to be offended – which says it all." It also received support from the British Humanist Association, the National Secular Society, the National Federation of Atheist, Humanist and Secular Student Societies and the New Humanist magazine. The society said it had been astounded by the "unending support".

The student union said it had "a duty to foster and encourage freedom of expression among our members, ensure diversity of our membership is recognised and pursue equal opportunities for our members".

The society had been asked to remove the advertisement "because UCLU aims to foster good relations between different groups of students and create a safe environment where all students can benefit from societies regardless of their religious or other beliefs".

The union had a duty to ensure students were not harassed because of characteristics which may make them appear different to others, including race, gender, religion, nationality or sexual orientation.

The atheist society said it would resist any disciplinary action. "Unfortunately, the union has considered the possibility that posting the image might have constituted an act of bullying, prejudice, harassment or discrimination," it said. "We firmly believe in the protection of our fellow students through university and union policy; however we cannot accept such a suggestion."

The society's president, Robbie Yellon, said he believed disciplinary action was unlikely and dismissed the idea that the society could be guilty of bullying or harassment. "As far as I, and the society, is concerned, that's an absolutely shocking accusation. If it does happen we will face it and do everything in our power to fight it."