The leader of a Muslim youth organisation and several senior politicians today condemned Prince Harry for a video diary in which he describes an Asian member of his platoon as "our little Paki friend".
The prince, who is third in line to the throne, made the comments in footage shot while training as an officer at the Sandhurst military academy in 2006, a year after being forced to make a public apology for wearing a Nazi swastika at a fancy dress party. Last night, St James's Palace issued a public apology for the latest incident, saying: "Prince Harry fully understands how offensive this term can be, and is extremely sorry for any offence his words might cause."
"However, on this occasion three years ago, Prince Harry used the term without any malice and as a nickname about a highly popular member of his platoon. There is no question that Prince Harry was in any way seeking to insult his friend."
The Conservative leader, David Cameron, became the first leading politician to comment on the matter when he told the BBC: "It is obviously a completely unacceptable thing to say and it is right that he has apologised.
"I think that it is important in the great institutions, whether it is the army or whether it is political parties, we have had to root out attitudes ... and that has to go right across the institutions."
But Cameron went on to say that he did not believe the prince should face further punishment: "He has made an apology. I think it is important he is clear about that and I think that is enough."
The Liberal Democrat leader, Nick Clegg, told Sky News the remarks "will have caused considerable offence".
Mohammed Shafiq, director of Muslim youth organisation the Ramadan Foundation, said the comments would be offensive to many Asians.
"The use of this sort of racism has no justification and I am saddened by those that are advocating using this term is not racist," he said.
"Prince Harry, as a public figure, must ensure that he promotes equality and tolerance and this rant, whether today or three years ago, is sickening and he should be thoroughly ashamed of himself."
In the film, the 24-year-old prince calls an officer from the Pakistani army, who was on the course with him, "our little Paki friend", and when he sees another officer cadet wearing a camouflage veil, exclaims: "Fuck me, you look like a raghead."
He also mocks the Queen – the commander-in-chief of the British army – during a pretend mobile phone call. "I've got to go, got to go," he says, while being filmed pretending to finish a call to her. "Send my love to the corgis. Send my love to the corgis and Grandpa. God save you ... yeah, that's great."
The video footage was released by the News of the World newspaper last night.
A Ministry of Defence spokesman said last night: "This sort of language is not acceptable in a modern army. Neither the army nor the armed forces tolerates inappropriate behaviour in any shape or form. The army takes all allegations of inappropriate behaviour very seriously and all substantive allegations are investigated."
The Equality and Human Rights Commission has demanded a formal inquiry into the prince's behaviour, and Muslim groups and leading MPs have warned the comments could increase tensions with Islamic groups in the UK.
Khalid Mahmood, the Labour MP for Perry Barr in Birmingham, said: "This might have been said in a lighthearted manner but ultimately it's offensive to a lot of people.
"He needs to understand that this is not acceptable, especially in light of the office that he is going to hold in the army and as a member of the royal family."
The film will infuriate army chiefs, who are actively trying to recruit Muslims as intelligence officers and translators for the campaigns in Iraq and Afghanistan. Staff officers have insisted the army's policy must be "zero tolerance to all forms of discrimination". But the casual use of racist terms by the prince, who was promoted to lieutenant last year, appears to add weight to recent claims by a Jamaican-born soldier that he faced regular racist abuse from non-commissioned and senior officers.
In September, three army instructors were suspended after an undercover BBC investigation into the infantry training centre at Catterick in Yorkshire. During the programme, one recruit was secretly filmed yelling "Paki" as he plunged his bayonet into a target dummy.
The prince's video begins as he joins other cadets gathering at an airport for their flight to Cyprus. He is behind the camcorder, panning over snoozing soldiers when he zooms in on the face of a Pakistani soldier. "Ah, our little Paki friend ... Ahmed," he whispers.
The trainee officer is thought to be Ahmed Raza Khan, who served with Prince Harry at Sandhurst for one year as a Commonwealth cadet.
Iftikhar Raja, from Croydon, south London, who told BBC Radio Five Live that he was Khan's uncle, said he expected better from the royal family. "At no time he told us that he was called Paki or he was a good friend of Prince Harry, I mean, although they served together that is true.
"I am proud to be British and if someone called me Pakistani I would be proud to be called that, but Paki is definitely a derogatory remark. We expect better from our royal family on whom we spend millions and millions of pounds for training and schooling."
The second remark comes after arriving in Cyprus. Prince Harry is again filming his comrades when one puts what appears to be some camouflage over his head. The prince says: "It's Dan the Man ... fuck me, you look like a raghead."
In another piece of footage, he gives orders to his comrades on an upcoming exercise. When he asks if there are any questions, one says: "Are your pubes ginger too?" The prince replies: "Yes they are," to laughter from the rest.
Later, again holding the camera, he asks another member of the squad to talk through the exercise they have just done. He asks for "your ups and downs in the exercise. Highs and lows ... good points, bad points." Off camera, he adds: "How do you feel? Gay? Queer on the side?"
Prince Harry, who is training to become an army air corps helicopter pilot, served on the frontline in Afghanistan last year in what was widely seen as a public relations triumph for him and the British army.