• Prime minister says 'hate' is not their motivation • FA had warned of possible criminal charges

The prime minister, David Cameron, has weighed into the delicate debate over whether Spurs fans should be punished for using "the Y-word" by contradicting the views of the Football Association and anti-racism group Kick It Out and backing their right to sing it.

The FA released a statement last week strongly restating its belief that the term "Yid" should not be used in any context at a football ground and warning that its use could amount to a criminal offence that would leave fans at risk of being banned and prosecuted.

The FA's stance was backed by the Board of Deputies of British Jews and the Community Security Trust, which represents Jewish interests, but Cameron said Spurs fans – who argue that they are reclaiming the word from those who use it to insult them – should not be punished for doing so.

"You have to think of the mens rea. There's a difference between Spurs fans self-describing themselves as Yids and someone calling someone a Yid as an insult," Cameron told the Jewish Chronicle.

"You have to be motivated by hate. Hate speech should be prosecuted – but only when it's motivated by hate."

In its original statement, the FA said the use of the term was still liable to cause offence, no matter who it was used by, and that its rules on language should be understandable and applicable to all.

"As such, the FA considers that the use of the term 'Yid' is likely to be considered offensive by the reasonable observer and considers the term to be inappropriate in a football setting," it said.

"The FA would encourage fans to avoid using it in any situation."

But the statement was ignored by large sections of the White Hart Lane crowd during Tottenham Hotspur's home victory over Norwich on Saturday. Fans loudly chanted "Yid army" and "We're Tottenham Hotspur, we'll sing what we want".

The FA and Spurs declined to comment on Cameron's contribution to the debate beyond referring to their earlier statements on the issue.

"The debate on this issue has two key considerations. Firstly, whether or not its use now plays a role in deflecting or attracting unjustified abuse, abuse that is inexcusable on any grounds; and secondly, whether it is liable to cause offence to others even if unintentionally," said a Spurs spokesman.

"Our fans have themselves engaged in this debate following the events of last season."

The club is conducting a widespread consultation with fans, including but not confined to season ticket holders, to gauge their views on the issue.

"We recognise that this is a complex debate and that, in the interests of encouraging a positive and safe environment for all supporters, consideration should be given to the appropriateness and suitability of its continued use," said the spokesman.

"We are already in the process of engaging with our fans and shall be consulting more widely in due course."

Kick It Out previously ran a high-profile campaign to try to stamp out the use of the word by fans of all clubs, led by a hard-hitting film made by the Chelsea fan David Baddiel, who is also Jewish.