Tony Blair has urged London mayor Ken Livingstone to apologise for his "Nazi" comment to a Jewish reporter.
Ken Livingstone has refused to apologise for the remarks
Labour's Mr Livingstone, who says he is "standing by" his remarks, had accused an Evening Standard journalist of being like a "concentration camp guard".
Mr Blair told Five's Wright Stuff show: "Let's just apologise and move on."
Mr Livingstone has said the remarks may have been offensive but were not racist, and said he would not apologise even if the prime minister asked.
On Wednesday he refused to make further comment as he was dealing with the International Olympic committee's four-day tour to assess London's Bid for the 2012 Games.
Instead, he repeated his view that the Holocaust was "the greatest racist crime of the 20th Century and Nazism the greatest evil in history". He also despised anti-Semitism.
However, Mr Blair, who was instrumental in returning Mr Livingstone to the Labour Party, insisted it was time for the London mayor to say sorry.
"A lot of us in politics get angry with journalists from time to time, but in the circumstances, and to the journalist because he was a Jewish journalist, yes, he should apologise," he said.
"Let's just apologise and move on - that's the sensible thing."
In a later interview on Five, the prime minister said he did not believe Mr Livingstone's job was on the line or that the mayor's remarks were meant to be anti-Semitic.
"I am quite sure he did not mean anything remotely anti-Jewish or anti-Semitic about it at all but it's a remark that can cause offence to people and it's best, if that happens, just to accept that, apologise and move on.
"It's difficult sometimes in politics but occasionally you have got to know when to say sorry and that's the only way of dealing with it."
'German war criminal'
Tory leader Michael Howard, asked about Mr Livingstone's remark by reporters, said it was important for politicians to be mindful about the language they use.
"It's particularly important that as we get close to the election that politicians talk with civility and courtesy about issues that we all face," he said.
"I think it's a matter of sadness that we are not seeing that from the Labour Party. We had what Ken Livingstone said, we had what Alastair Campbell has said and we have what others have said. I think that's a matter of great regret."
The row blew up after Mr Livingstone was approached by Evening Standard reporter Oliver Finegold following a party marking the 20th anniversary of former Culture Secretary Chris Smith coming out as Britain's first gay MP.
On tape, Mr Livingstone, who once worked as a freelance restaurant critic on the paper, is heard asking Mr Finegold if he is a "German war criminal".
Mr Finegold replies: "No, I'm Jewish, I wasn't a German war criminal. I'm quite offended by that."
The mayor then says: "Ah right, well you might be, but actually you are like a concentration camp guard, you are just doing it because you are paid to, aren't you?"
At his weekly press conference on Tuesday, Mr Livingstone said his comments were not racist and refused to apologise.
"If you think they are racist, I think you are wrong," he told reporters.
An official complaint has been made to local government watchdogs by the Board of Deputies of British Jews, demanding an investigation by the Standards Board of England.
It has the power to suspend or bar Mr Livingstone from public office.