Former royal butler Paul Burrell has refused to return to the inquest into the death of Diana, Princess of Wales.
Paul Burrell says he has no plans to be in the UK in the near future
He had been asked to explain discrepancies between his evidence and comments reported in the Sun newspaper.
In a video recording obtained by the Sun, Mr Burrell apparently claims he introduced "red herrings" during his evidence and held back facts.
The coroner said he cannot compel him to give evidence because he is outside the court's jurisdiction in the US.
Lord Justice Scott Baker said in a statement: "The coroner asked him to give further evidence either in person or via videolink from abroad.
"Mr Burrell has refused to do this and, as he is outside the court jurisdiction, the coroner has no power to compel him to give evidence."
'Play the game'
Mr Burrell's conversation was recorded in a New York hotel on 18 February after he gave evidence to the inquest a month before.
Sections of the transcript of the conversation have been read to the jury at the High Court.
In it, Mr Burrell said he had made the 500-mile round trip from London to his home in Cheshire to pick up documents for the coroner because he had to "play the game".
In the transcript, Mr Burrell said: "I sacrificed my own integrity for the bigger picture, but people are wise enough to realise that.
"Perjury isn't a very nice thing to have to consider."
A witness statement made on 26 February was also read to the jury, in which he said in his evidence to the inquest he had not concealed "anything remotely relevant to the inquiry".
"I accept that whilst I was under cross-examination my evidence may at times have strayed from the strictly relevant, but at no time did I tell any untruths."
He said when the conversation took place he was "tired and depressed and had been drinking all evening".
During the conversation, he was "showing off", he added.
"I am not proud of this. I was trying to impress him. The comments I made to him were not correct."
Court officials have said an investigation into whether he committed perjury was not in the coroner's remit.
At the time of his three-day appearance at the inquest in January, Mr Burrell described the experience as "horrid".
Meanwhile, the coroner told the inquest that it was "a mystery" that no photographs existed of Diana's final car journey prior to the crash in Paris which killed her, Dodi Al Fayed and driver Henri Paul in 1997 - even though the vehicle was pursued by paparazzi.
But picture agent Laurent Sola, whose photographers were working on the story that night, said any unclear pictures would have been discarded.
"If there were photographs of Princess Diana and they were not clear or blurry they would be cut off and thrown away," he said.
The coroner replied: "It does seem a bit odd that all the photographers seem to have had the same problem, if they took any photographs."
The hearing continues.