Shadow minister Naz Shah said she would have "done things differently" to root out anti-semitism in the Labour party.
Speaking at a Jewish hustings event, organised by Jewish News, Jewish Chronicle and the Board of Deputies, Ms Shah admitted she would have dealt with anti-semitism in a different manner compared to Labour leader Jeremy Corbyn.
The Shadow Minister for Women and Equalities said: "When I went on my journey, for me it was really important to make an unequivocal apology.
"I'd have done things differently, I'd want the Labour party to go on the same journey.
"Labour members, some not all, need to go on that journey and there are people in other political parties that need to go on that journey."
The Bradford West MP shared a Facebook post in 2014 which suggested Israel should be relocated to America, with the comment "problem solved."
She was also accused of writing "the Jews are rallying" on her Facebook page.
Ms Shah was suspended from her party and had the parliamentary whip removed in 2016 amid the anti-semitism accusations.
The Labour MP later said she had been "ignorant" about discrimination against Jews and admitted the language she used had been anti-semitic.
Speaking at the hustings event, alongside Tory Robert Jenrick and Lib Dem Chuka Umunna, Ms Shah said: "One of the reasons I came here tonight was because I recognise where we're at.
"I recognise my responsibility and my position as leadership as equalities [sic] to put my money where my mouth is and come here and listen." She said she believes Mr Corbyn "does care" about anti-semitism and dealing with it within the Labour party.
But she added: "Whether he does it the right way and whether he's getting it right is a different question and that's a conversation that I want to continue with the leadership.
"We should have acknowledged a lot more, we should have done a lot more and we didn't, had we done that in the first instance, I wouldn't be answering these questions today."
The Labour leader apologised for the party's handling of anti-semitism in an interview on This Morning on Tuesday.
He said: "Our party and me do not accept anti-Semitism in any form... obviously I'm very sorry for everything that has happened.
"But I want to make this very clear: I am dealing with it, I have dealt with it, other parties are also affected by anti-Semitism."
Ms Shah said Mr Corbyn is "putting things in place" to deal with anti-semitism but "the idea that we have thousands of complaints isn't true."