Prince Harry and Ahmed Raza Khan, bottom, at Sandhurst in 2006
Gordon Brown has said he believes the British public will give Prince Harry the "benefit of the doubt" after he apologised for using racist language.
Mr Brown told GMTV he saw Harry's apology as genuine, after the prince was captured on film calling a fellow cadet "our little Paki friend" in 2006.
Labour MP Keith Vaz said the term was "unacceptable and wounding".
The defence secretary said Harry's commanding officer was likely to speak to the prince in the next few days.
John Hutton told the Commons: "We should not lose sight of one very important fact in all this, that Prince Harry has served his country on active service in Afghanistan and I believe very strongly that there is no better example of public service than that."
The comment was in a home video Prince Harry made when he was an officer cadet in 2006 and which was obtained by a Sunday newspaper.
Speaking on GMTV, the prime minister said his comments had "no part in our life".
"It was a mistake and he's made the admission of that..." he said.
"... the British people are good enough to give someone who has actually been a role model for young people and who has done well fighting for our country... the benefit of the doubt," Mr Brown said.
Although he did not think Prince Harry was a racist, Labour MP Keith Vaz told BBC Radio 4's Today programme that he should spend more time with his father, who had "shown how much can be done to build relations between communities".
"We cannot use language of this kind, even in jest," he said.
"He is not an understudy for Bernard Manning. He is third in line to the throne; he is a role model."
Rod Richards, who served as a Foreign Office minister in former prime minister John Major's Conservative government and also as an officer in the Royal Marines, defended the prince on the Today programme.
He said he regarded "Paki" as an abbreviation, and the prince, in his view, had "not crossed the line".
Welshman Mr Richards added that he was frequently called "Taffy" in the Army, and even in the House of Commons a colleague used to make references to him "having sexual relations with sheep".
The father of the soldier involved has also criticised the prince for using what he called a "hate word".
Muhammad Yaqoob Khan Abbasi spoke to the Daily Mail from his home in Pakistan, and condemned the prince's comment about his son, Ahmed Raza Khan.
October 2008 - 6.3% or 12,088 personnel in the Armed Forces were from an ethnic minority
April 2008 - 6.1% or 11, 753
October 2007 - 5.9% or 11, 434
April 2007 - 5.8% or 11, 349
April 2006 - 5.5% or 11, 058
April 2005 - 5.3% or 10, 943
Source: Ministry of Defence
He told the newspaper: "When I saw the video I was very, very hurt. I strongly condemn the fact that Prince Harry used that language against my son.
"That word he used is a hate word and should never be used against any Pakistani.
"Prince Harry should apologise to the Pakistani Army and to the Pakistani government for this. I cannot accept his apology unless they first accept his apology."
In the Commons, Labour MP Diane Abbott said it would be a "shame" if the incident undermined efforts in the military to recruit from "diverse communities".
And Labour MP Harry Cohen suggested the prince's comments would deter people of Pakistani origin from joining the military.
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