King Charles declared his eldest son, Prince William, Prince of Wales during his first speech as monarch the day after the death of Queen Elizabeth II.
Prince William's wife, Catherine, became Princess of Wales, the first time the title has been held by anyone since Princess Diana.
King Charles had held the title since he was nine, with his investiture taking place in 1969 at Caernarfon Castle when he was 20.
Protests at the time coincided with the ceremony, including a bomb plot coordinated by a Welsh paramilitary group.
Now the King’s decision to bestow the title on to his son has sparked some debate in the country.
The online petition, which continues to gather supporters, reads: “The title remains an insult to Wales and is a symbol of historical oppression.
“The title implies that Wales is still a principality, undermining Wales’ status as a nation and a country.
“In addition, the title has absolutely no constitutional role for Wales, which is now a devolved country with a national Parliament.”
Wales’ First Minister Mark Drakeford said there is an "alive" debate surrounding the role - but told ITV's Sharp End he won't be taking part in it "this week" during the period of national mourning.
Plaid Cymru leader Adam Price said he believed the people of Wales should have the "final say" on the whether the title is used.
In a tweet last Friday following King Charles III's announcement, Mr Price said: “It is Plaid Cymru’s long held view that it should be the people’s democratic right to have a final say on this matter in an independent Wales.
“For now, Plaid Cymru’s thoughts are with the Royal Family as they grieve.”
The last native prince of Wales was Llywelyn Ap Gruffudd, also known as Llywelyn the Last, who was the prince of Gwynedd.
Llywelyn was killed by English soldiers in 1282 and almost 30 years later Edward I gave the title to his son Edward II.
Since then the title has been reserved for the heir to the British throne, however there have been long periods when the title has not been used.
'A future that is full of promise'
On Friday, the King will visit Wales for the first time since his ascension to the throne.
One of the locations the King will visit in Cardiff, Llandaff Cathedral, has been rumoured by the Telegraph to be where the investiture of the new Prince of Wales could take place next year.
A statement released by Kensington Palace said the new Prince and Princess of Wales would “do their part to support the aspirations of the Welsh people”.
“The prince and princess look forward to celebrating Wales’s proud history and traditions as well as a future that is full of promise.”