The 65,000-tonne aircraft carrier left Portsmouth Naval Base on Saturday before an “emerging mechanical issue” occurred.
Its departure had already been delayed, on Friday August 26, due to an unforeseen technical issue.
The Royal Navy has not offered further details, or confirmed if the technical issue on Friday was linked to the mechanical problem reported on Saturday.
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 £3billion vessel is sailing to undertake training exercises with the US Navy as well as the Royal Canadian Navy and United States Marine Corps.
The programme is expected to include exercises with the F-35B Lightning jets.
Departing on Saturday afternoon, the NATO flagship passed thousands of music-lovers at the Victorious music festival on Southsea Common in Portsmouth.
Sugababes performed as the ship sailed past, with the crew lining the flight deck to get a view of the festival.
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.”
HMS Prince of Wales
POPhot Jay Allen/Ministry of Defence/Crown Copyright
The Royal Navy's flagship in Gibraltar
LPhot Mark Johnson/Ministry of Defence/Crown Copyright