However, as the mayor faces a possible investigation by the local government watchdog, the Standards Board for England, he is standing firm and refusing to offer an apology for calling the reporter, Oliver Finegold, a "concentration camp guard" at a party following a heated exchange.
The mayor's office has accused the Evening Standard of harassment as the two parties exchange the latest in a long-running series of blows.
Jowell, speaking on television on Sunday, said Livingstone could apologise for losing his temper but added she did not think he was either racist or anti-Semitic. She placed part of the blame on Finegold.
"I don't believe he has a racist or an anti-Semitic bone in his body - look at his political record," said Jowell.
"Sometimes he has a filthy temper and I think he lost his temper because he was door-stepped in an aggressive way. I think it is always a good idea that, if you lose your temper, it is good to apologise."
The Board of Deputies for British Jews said it would refer Livingstone's remarks to the Standards Board, which has the power to ban public figures from office for as long as five years.
Livingstone also faces censure from the London Assembly this week. The assembly's Tory leader, Brian Coleman, has tabled an emergency motion calling on the mayor to apologise and withdraw his comments.
"All reasonable people think the mayor has gone too far. His original remarks were deeply offensive. He then compounded the situation by refusing to apologise. This entire episode has been a failure of civic leadership in his behalf," he said.
The argument between Finegold and Livingstone took place at a party celebrating the 20th anniversary of former culture secretary Chris Smith coming out as the first openly gay MP.
The reporter taped the conversation and Livingstone is heard asking Finegold if he were a "German war criminal" before he told him he was like a "concentration camp guard".
Livingstone is said to have told the reporter that he should work for a paper "that doesn't have a record of supporting fascism".
The comment was a reference to the Standard's sister paper, the Daily Mail, which in 1934 ran a front-page story declaring "Hurrah for the Blackshirts".
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