David Cameron will apologise to the Queen after he was overheard saying she "purred" on hearing the result of the Scottish independence referendum.
A camera crew recorded the PM telling former New York Mayor Michael Bloomberg he had "never heard someone so happy" as the Queen after Scotland voted "no".
Mr Cameron has said he is "embarrassed" and "extremely sorry" for the remarks.
He has contacted Buckingham Palace and will apologise in person when he next meets the Queen, Downing Street said.
Buckingham Palace has not commented.
Last Thursday, Scottish voters rejected independence from the UK by 55% to 45%.
Speaking in New York, Mr Cameron told Mr Bloomberg he had phoned the Queen to tell her the result.
"She purred down the line," he said. "I've never heard someone so happy."
He added: "It should never have been that close.
"It wasn't in the end, but there was a time in the middle of the campaign when it felt... I've said I want to find these polling companies and I want to sue them for my stomach ulcers because of what they put me through, you know. It was very nervous."
Following the referendum result, the Queen said she believed Scotland would unite in a "spirit of mutual respect and support", despite "strong feelings and contrasting emotions".