Farron told the BBC's Sunday Politics: “I’m in favour of that Act, I was also challenging it, as many other Liberals did.
“And by the way, Peter Tatchell was on the same side as me, many others were as well, who thought it is right that you stand up in favour of protecting minority rights in these circumstances.”
But on Monday Tatchell rebuked Farron, saying they were "absolutely not on the same side".
"Maybe he's just misremembered and it was unintentional," he said, "but he doesn't have a good record across the board.
"He abstained from one of the key votes on same sex marriage and it doesn't look good for him to now be portraying himself as someone who's long supported gay rights.
"There's no doubt that he voted against the anti discrimination laws to protect LGBT people in 2007 and he wanted exemption for religious organisation under the Equality Act 2010.
"I did not support either of those positions and I said so very publicly."
Farron was quick to back down over his remarks made the previous day, apologising, and saying he had "misremembered" Tatchell's position.
"I do apologise without reservation if I have misremembered Peter Tatchell’s position," he said.
“But to be clear I do believe if you provide a service it must be offered on an equal basis and if this comes up again I will vote accordingly.”
But the LGBT rights campaigner called on the Lib Dem MP to go further and show he was truly behind backing equality legislation.
He told the BBC's Daily Politics: "I want to see a really strong commitment from Tim - not just an apology - I want to see action.
"Action in terms of supporting new legislation to remedy the remaining inequalities in legislation, such as the fact that the Equality Act still does have religious exemptions, and it would be great if he could say that he respects people's right to hold religious beliefs, but, like me, thinks religious people should be bound by the same duty not to discriminate against everyone else."