The Prime Minister says he believes Prince Harry is genuinely sorry for using a racist word to describe a Pakistani member of his army platoon.
The prince apologised after a newspaper published the video of him using the term when he was training to be an Army officer in 2006.
Harry said he used the word as a nickname for a fellow soldier, and didn't mean it as an insult.
But the soldier's father said he was "very hurt" Harry had used the word.
Speaking from his home in Pakistan, Muhammad Yaqoob Khan Abbasi said: "When I saw the video I was very, very hurt.
The PM believes Harry is really sorry
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"That word he used is a hate word and should never be used against any Pakistani."
The Army has said it isn't launching a formal investigation into the matter, because no complaint has been made.
Speaking on TV, Prime Minister Gordon Brown said Harry had made a mistake.
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."
Role model
But Labour MP Keith Vaz said although he didn't think Harry was racist, language like that should never be used.
"He is third in line to the throne, he is a role model," he added.