"Mr Corbyn said that Mr Livingstone's remarks would be investigated and dealt with by Labour's General Secretary and National Executive Committee.
And the Labour leader told the BBC: "It's not a crisis. There's no crisis. Where there is any racism in the party it will be dealt with and rooted out. I have been an anti-racist campaigner all my life."
Asked, during an election visit to Hull, whether the party had a "problem with anti-Semitism", Mr Corbyn replied: "No, there is not a problem. We are totally opposed to anti-Semitism in any form within the party.
"The very small number of cases that have been brought to our attention have been dealt with swiftly and immediately, and they will be."
Mr Livingstone's suspension came after he took to the airwaves for a series of interviews in an attempt to defend Bradford West MP Naz Shah from allegations of anti-Semitism.
Ms Shah was suspended on Wednesday pending an investigation into controversial social media posts about Israel which she made before becoming an MP.
But Mr Livingstone insisted that while her remarks were "over the top", she was not anti-Semitic, and that he had never encountered anti-Semitism in 40 years in the Labour Party.
He sparked fury among colleagues by going on to claim that Hitler had supported Zionism "before he went mad and ended up killing six million Jews"."
Ironically it's the other half of Livingstone's statement that in a sane society would be subject to critical thought.