The Duke of York responded to the statement given by the police, in which they apologised for the inconvenience caused.
"The police have a difficult job to do, balancing security for the royal family and deterring intruders, and sometimes they get it wrong," said the prince. "I am grateful for their apology and look forward to a safe walk in the garden in the future."
Prince Andrew was enjoying a stroll in the palace grounds when he was stopped and asked to verify his identity, just two days after an attempted burglary took place at Buckingham Palace.
In a previous statement, the police confirmed that they had stopped a suspected intruder but did not specifically name him as Prince Andrew. Despite reports by The Sunday Express that the British royal was held at gunpoint and ordered to "put [his] hands up and get on the ground," the police denied using any force.
"On Wednesday 4 September at approximately 18:00 BST two uniformed officers approached a man in the gardens of Buckingham Palace to verify his identity," read the statement. "The man was satisfactorily identified. No weapons were drawn and no force was used."
According to the newspaper, an internal inquiry has been carried out, although Buckingham Palace has made no comment.
The incident occurred two days after an attempted break-in at the royal residence. The Queen and Prince Philip were not in the palace at the time, as they are currently on their summer holiday at Balmoral.
Two men, who were thought to be after the Coronation jewels, were arrested for burglary, trespass and criminal damage. DJ Victor Miller, 37, was reportedly taken in by police and passed into the care of mental health professionals, while his suspected accomplice was released on bail.
Monday's incident is the worst breach of security at the Palace since 1982 when unemployed father-of-four Michael Fagan climbed up a drainpipe and broke into the Queen's bedroom.
The Queen, who was in bed at the time, spent 10 minutes speaking to the intruder before he asked for a cigarette which allowed her to call a footman, who called the police.
Buckingham Palace is monitored by CCTV and surrounded by a wall and a fence, both of which are covered in anti-climb devices.
The building is also permanently guarded by armed officers from the Royal and Diplomatic Protection Unit and further members of security are also present within the Palace itself.