The lord chancellor has said there is no need for Prince Harry to make in person a second apology over wearing a Nazi costume to a fancy dress party.
Prince Harry has earned a reputation as the 'party prince'
The prince apologised in a statement after being photographed wearing the desert uniform and swastika armband.
But Conservative leader Michael Howard has led calls for a public apology.
Lord Falconer told BBC One's Question Time: "He apologised straight away after the mistake became public. I think we should leave it at that."
The photograph, taken at a friend's birthday party in Wiltshire at the weekend, has prompted outrage from politicians and anti-fascist campaigners who accused the prince of insensitivity.
In his statement on Wednesday, the prince said: "I am very sorry if I caused any offence or embarrassment to anyone. It was a poor choice of costume and I apologise."
Tory leader Michael Howard and Liberal Democrat leader Charles Kennedy said on Thursday that Prince Harry should say sorry in person.
Mr Howard told BBC Radio 4's Today programme that the prince should "tell us himself how contrite he now is".
The Queen's former assistant press secretary, Dickie Arbiter, said a personal apology was needed if Prince Harry wished to be considered an adult.
But Lord Chancellor, Lord Falconer told Question Time: "I don't think he needs to make a public apology. I think already he must understand what has happened and I think that should be the end of it."
Clarence House said there were no plans for the prince to say more.
The UK's Chief Rabbi Jonathan Sacks said it was imperative that the lessons of the Holocaust and Second World War were not only taught, but understood.
He added that wearing a swastika was in extremely poor taste but added: "I note that Prince Harry has recognised this."
Earlier this month the prince was helping with the tsunami relief effort
Some said the prince should join a British delegation which is visiting the Auschwitz death camp for the 60th anniversary of its liberation later this month.
Prince Harry should see for himself "the results of the hated symbol he so foolishly and brazenly chose to wear", said Rabbi Marvin Hier, founder of Jewish human rights group the Simon Wiesenthal Center.
Unusually, the prince's actions have been criticised by foreign politicians.
Israel's foreign minister Silvan Shalom said the prince was wrong to wear the costume and had a lot to learn.
It is the latest in a series of stories involving 20-year-old Prince Harry, who is third in line to the throne, which have earned him a media reputation as the "party prince".
Mr Arbiter said that had the incident happened on his watch he would have thrown his hands up in "absolute horror" and thought "here we go again".
"It's just not good enough to behave like that. We all know history, and at 20 there is no excuse," he said.
Prince Harry's gaffe has also prompted suggestions from some that he should not be allowed to enrol at Sandhurst military academy.
The Ministry of Defence has said it will not affect his place.
The Jewish Chronicle said that for a royal to think it a "lark to dress up in the trappings of a genocidal dictatorship" was "mind-boggling".
But the Board of Deputies of British Jews said while the costume was in bad taste, members were "pleased" Prince Harry had apologised in a statement.
And Rabbi Dr Jonathan Romain, of the Reform Synagogues of Great Britain, said the apology should be accepted.
Writer Moyra Bremner told BBC News 24 it was extraordinary no-one had stopped the prince wearing the costume and said it was "a terrible error of judgement".
But she added: "I don't think for an instant he meant any insult to Holocaust survivors or indeed the many people who were killed in the concentration camps and the many people in the [British] services who were killed."