But he said the rise in antisemitism was "worrying, a deep cause for concern".
He expressed a number of "reservations" about Shami Chakrabarti's inquiry into antisemitism in the Labour Party, saying some elements had been "disappointing".
Rabbi Mirvis said he could not understand why Ms Chakrabarti's report had not included details of Baroness Royall's own report on allegations of antisemitism at Oxford University Labour Club.
"One wonders, what is there to hide? The outstanding track record of the Labour Party leads us to have added concerns, why has there been a shift in the recent past? We need to encourage the party to get back on track.”
There was, he said, an "apparent indifference" among the party's leadership about tackling the problem.
Asked by Keith Vaz, committee chair, about the influence of social media, the Chief Rabbi said it was "part of the problem, but not the whole problem".
He called on social media companies to do more to stop antisemitism appearing on their sites and said he believed companies should introduce filters to block such hatred.
The Chief Rabbi also voiced his concern about the rise of hate crime in Britain since the European Union referendum last month.
Rabbi Mirvis was speaking ahead of Sir Mick Davis, Jewish Leadership Council chairman and Mark Gardner, Community Security Trust communications director.
Mr Gardner told the panel of MPs that CST raised £7 million a year to help protect British Jews, in addition to receiving government funding.
Sir Mick said that he had been labelled a "self-hating Jew" for expressing his concerns about the government of Benjamin Netanyahu in Israel.
On anti-Zionism, Sir Mick added: “Zionism is so totally associated with how the Jew sees himself – if you attack Zionism, you attack the very way in which Jews see themselves. It is perfectly possible to be a Zionist and believe in the rights of the Palestinian people to their own land.
“I do not believe today that you can be against Zionism and not be antisemitic”.
Sir Mick praised the interfaith efforts of Sadiq Khan, the new London mayor.
He claimed that since 2010, there had been 97 early day motions set up in Parliament to criticise Israel, compared to 16 on Syria and nine against North Korea.
They were followed by John Mann, Labour MP and chair of the All-Party Parliamentary Group Against Antisemitism.
Mr Mann outlined the abuse he had received while in his APPG role. He had been accused of having a "puppet master" and "taking money" to raise issues about antisemitism.
"There is a particular insidiousness when it comes to antisemitism," he added.
Mr Mann was asked about the Chakrabarti report and Jeremy Corbyn's response to it. Mr Mann said: "If he can see through the Chakrabarti report and implement it, that would be significant.
"In particular the use of the word 'Zio', the use of 'Nazi' in reference to Israel and the use of 'Zionist' as term of abuse and insult – if those three are delivered that would be a very significant breakthrough.
"If he can deliver that, I would be first to say that he’s made a huge breakthrough."
He went on to say the role of party leaders in tackling antisemitism was to "sort out your own back yard".
Mr Mann was asked whether, having seen Ken Livingstone's evidence to the committee, he believed the former Mayor of London had clarified his statements on Hitler and Zionism.
"Not in the slightest," said Mr Mann.
Jeremy Corbyn, the Labour Party leader, gave evidence last week, following Jonathan Arkush – Board of Deputies president – and Angus Robertson, SNP MP.
Mr Livingstone was also questioned on his controversial statements on Hitler and Zionism.
Today's session concluded the committee's inquiry.
