The 65,000-tonne warship left from Portsmouth Naval Base, Hampshire, on Saturday before an “emerging mechanical issue” occurred.
A Royal Navy spokeswoman said: “HMS Prince of Wales remains in the South Coast Exercise Area while conducting investigations into an emerging mechanical issue.”
The vessel’s departure had earlier been delayed from Friday, August 26, because of a technical issue.
The Royal Navy was not able to offer any further details or confirm if the earlier technical issue was related to the mechanical problem.
Specialist website Navy Lookout has reported that the issue was caused by damage to the starboard propeller shaft although the MoD has not confirmed or commented on this.
The website says a photograph of the carrier leaving Portsmouth shows only a wake on the port side suggesting a problem with the other propeller shaft.
It states that, unless the problem can be resolved at sea enabling the warship to continue its journey to the US, it might need to go into dry dock at Rosyth, Scotland, early ahead of a planned inspection in 2023.
The £3 billion carrier had a colourful send-off as it departed on Saturday afternoon and passed thousands of music-lovers at the Victorious music festival on Southsea Common in Portsmouth.
Pop favourites Sugababes were in the middle of their set when the giant ship sailed past with the crew lining the flight deck to get a view of the festival.
The programme is expected to include exercises with the F-35B Lightning jets.
A Royal Navy spokesman said on Saturday: “HMS Prince of Wales will cross the Atlantic with her task group, ready to push the boundaries of un-crewed technology and the tactics used by the UK’s two new Queen Elizabeth-class carriers.
“Along with notable port stops in New York, Halifax in Canada, and the Caribbean, the next three months will see the Prince of Wales task group work closely with US allies, operating F-35B jets and un-crewed systems which will define Royal Navy aviation of the future.
“With fleet flagship HMS Queen Elizabeth also set to deploy to the Mediterranean and Baltic this autumn at the heart of a potent Royal Navy task group, it will mean both UK aircraft carriers will be operating F-35B jets thousands of miles apart.”