The BBC has apologised for revealing that the Queen raised concerns with the government about why radical cleric Abu Hamza al-Masri had not been arrested.
The apology comes after security correspondent Frank Gardner told BBC Radio 4 of a private conversation he had with the Queen some years ago.
The BBC said it and Gardner were sorry for the "breach of confidence", which both "deeply regret".
On Monday, Abu Hamza lost his latest appeal against extradition to the United States. The European Court of Human Rights ruled that the extradition could go ahead. The Home Office hopes this can be achieved within three weeks.
The Strasbourg court's decision means that the cleric and four other terrorism suspects can face terrorism trials in the US after delays as far back as the late 1990s. In the case of Abu Hamza, he was first arrested in 2004, the BBC reports.
The development was being discussed on Radio 4's Today programme on Tuesday morning when Gardner revealed details of his conversation with the Queen on the matter. He said the monarch had told him, in a private meeting, how she had been upset that Abu Hamza could not be arrested.
The radical cleric had risen to prominence for his sermons in and around Finsbury Park mosque, which gained wide media attention for their content.
Gardner said the Queen had told him she had spoken to a former home secretary about the case.
In a statement, the BBC admitted the conservation should have remained private and was "wholly inappropriate" that it was disclosed. It said Gardner was "extremely sorry for the embarrassment caused and has apologised to the Palace".
A spokesperson for Buckingham Palace said it would "never comment on private conversations involving any member of the Royal Family".
The Home Office also said it would not comment on such conversations.