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Gordon Brown today described as "unacceptable" the moment when Prince Harry zoomed his camcorder in on the face of a fellow Sandhurst cadet and mused: "Ah, our little Paki friend, Ahmed".

But the Prime Minister predicted that the British public would give the prince the benefit of the doubt over his use of racist language in the 2006 home video.

The footage has triggered a furore since it was obtained by the News of the World and published yesterday. The father of Ahmed Raza Khan, now a captain in the Pakistan military, accused Harry of using a hate word, and demanded that he apologise to the Pakistani army and the Pakistan government.

St James Palace has issued a statement of apology on the prince's behalf, saying that Harry fully understood how offensive the word Paki could be and was extremely sorry for any offence caused.

Today Mr Brown put his own gloss on the controversy, which has prompted 25 per cent of those who voted in a Times Online poll to call for the prince to be sacked from the army.

In the film, part recorded by the prince and part by army comrades, Prince Harry also tells a fellow cadet who has swathed his head in cloth during a night exercise in Cyprus: "F*** me, you look like a raghead" - an offensive word for an Arab which St James Palace said the prince had meant to refer to the Taleban.

"I think Prince Harry knows that these comments are unacceptable and I think he has made an apology," said Mr Brown.

"I think it is a genuine apology. These comments have no part in our life and I think he is meeting his commanding officer quite soon to talk about it.

"It was a mistake, he has made the admission of that and, once he has made his apology, I think the British people are good enough to give someone who has actually been a role model for young people and has done very well fighting for our country, gone into very difficult situations with bravery, I think they will give him the benefit of the doubt."

The home video appears to be a jokey record of Harry and his friends' training days. The comment about Captain Khan appears in footage of cadets sleeping sprawled on the floor at an airport as they are sent to Cyprus, while other scenes are shot outdoors during military exercises.

In one extract, the prince is seen entertaining his fellow cadets during a briefing by pretending to be on the phone to his grandmother, the Queen. "Love to the corgis... God save you," he says, causing soldiers in his platoon to laugh.

The Army has said that it has not launched an investigation into the incident as no formal complaint has so far been laid. Lieutenant-Colonel Harry Fullerton, the commanding officer of the Household Cavalry, Harry's regiment, has called the prince in for a dressing down.

Other politicians have condemned the footage. David Cameron, the Tory leader, said that saying the word Paki was completely unacceptable, while Lib Dem leader Nick Clegg said it had caused considerable offence, although as the prince had apologised it was now time to move on.

Keith Vaz, an Asian MP, questioned whether the prince's comments showed that there was a racist culture in the army. "Is this an explanation as to why we have so few ethnic minority people prepared to join institutions like the Army, because people in the Army regard such language as acceptable?" asked Mr Vaz.

He suggested that the prince take a leaf out of his father's book, as the Prince of Wales had done much to build relations between different faith communities.

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