During an appearance in Batley today, the Holborn and St Pancras MP also backed an "element" of independent decision-making in regard to investigations into racism in the party.
In a race that features four women candidates - and the party is yet to have a first female leader - he declined to name any leadership attributes which he felt elevated him above fellow hopefuls but reiterated that he would be able to unify Labour.
Batley and Spen MP Tracy Brabin told an audience at the West Yorkshire town's community centre that a reason she was backing Sir Keir in the leadership race was that people on the doorstep during the election campaign repeatedly said they would vote Labour if he was the head of the party.
After being asked about the subject during a question-and-answer session, Sir Keir said that he supported the international definition of anti-Semitism - the International Holocaust Remembrance Alliance guide is commonly used - but said: "I accept that some of the examples need to be looked at. But it was right to sign up to that definition."
An issue under Jeremy Corbyn's leadership has been whether the party should adopt the international definition in full, which it now has.
Sir Keir added that there were colleagues who were "not anti-Semitic in the slightest but they feel their reputation has been stained" by the issue.
After his speech, The Yorkshire Post asked what his first significant action as Labour leader would be to stamp out anti-Semitism.
The QC and former director of public prosecutions said: "Absolute clarity: if you're anti-Semitic, you shouldn't be in the Labour Party. And I would take a personal lead on this as leader of the Labour Party and ensure that I wasn't asking somebody else to take responsibility, that I was taking responsibility for it.
"I do think there are rule changes that we can make in the Labour Party, but most importantly we need to rebuild our trust with the Jewish community and I don't think we can do that until those that have left our party because of anti-Semitism feel comfortable to return to our party."
Asked what rule changes he envisioned, he said: "So far I've argued for the international definition of anti-Semitism, which we've now adopted, that those who are clearly anti-Semitic should be excluded much more quickly from our party and also that now the European Human Rights Commission are looking at the Labour Party, we should open our books and allow access to all our staff so that the commission can get right into the weeds of what the problems are and give us strong recommendations."
He added: "I am in favour of independence in the decision-making. Obviously what form that takes is something we'll have to discuss, but I think that it's hard to restore the trust of the Jewish community unless we have an independent element in there."
The Equality and Human Rights Commission (EHRC) announced in May last year that it was conducting an inquiry under section 20 of the Equality Act 2006 after carrying out preliminary investigations.
The Yorkshire Post has contacted the EHRC to clarify whether it already has access to all Labour Party staff during its inquiry.
Four women feature in the leadership contest - Jess Phillips, Emily Thornberry, Lisa Nandy and Rebecca Long-Bailey - and Sir Keir is the only man.
Ms Long-Bailey is this evening expected to say she would "end the gentleman’s club of politics" during her campaign launch, according to national reports.
Asked what leadership skills of his overrode the importance of Labour having a first woman leader, Sir Keir said: "I don't think any of the candidates are standing because they're a man or because they're a woman.
"Everyone is standing because they genuinely think that they would be the best leader of the Labour party to rebuild our party, to be that effective opposition and to find our way to next general election victory.
"Those are sincere cases made by all of the candidates. We're making different arguments and the members will decide between us but that's why we're doing this, because we care about the future of our party and the future of our country."
Probed further, he said: "I'm not going to compare myself to other candidates and suggest they don't have attributes, I'm really pleased that we've got excellent candidates.
"I think I have leadership skills, having run an organisation, having taken national decisions, I think I've got the ability to pull people together and to unite our party and the utter determination that we should win the general election."
Sir Keir, who studied law at the University of Leeds, stressed the importance of winning elections in being able to change people's lives during his packed-out speech.
As an example, he said that after being elected as an MP in 2015, he voted on issues 172 times in his first year, but lost on 171 occasions.
Questioned about whether he would break with socialism or his political morals to win at a future general election, he said: "I don't think that that's a choice we have to make. I see millions of people crying out for change in this country. In this general election I went to 44 constituencies. I didn't meet people who were saying: 'Things are fine, things are great, the health service - I like waiting for a doctor, I like the fact that our public services have been decimated'.
"Everybody wants fundamental change; they didn't trust the Labour Party to deliver it. And that's what we've got to do, restore trust in the Labour Party as a force for good and force for change."