The flags have appeared on lamposts and telegraph poles in predominantly unionist areas on the outskirts of the city, just days before the anniversary on the 30th.
Their appearance has have prompted widespread condemnation from both unionist and nationalist politicians.
Now, the regiment itself has branded the erection of the flags as “totally unacceptable and disrespectful behaviour”.
A spokesperson for the Parachute Regiment made the comment in a brief statement on Twitter, posted in response to a statement also condemning the action from UUP leader Doug Beattie.
Mr Beattie said: “The flying of the parachute regiment flag on the anniversary of Bloody Sunday it wrong.
“It does nothing but hurt the victims who still grieve to this day and shows a total lack of respect and compassion. Please take them down.”
DUP MLA Gary Middleton, meanwhile, also condemned the erection of the flags.
“I share the position of the Parachute Regiment,” the Foyle MLA said. “These actions are unacceptable and disrespectful. It is unnecessary and designed to be offensive. “
Mr Middleton went on to say: “I am British, I am proud of our Armed Forces being the best in the world.
“I am proud that our security forces helped defeat the PIRA but these flags are not designed to mark any of those things. I trust they will be removed just as many offensive republican flags etc need to be removed as well.”
SDLP leader Colum Eastwood said the flags have “caused real hurt and anger”.
He said: “This is a time where we should be supporting the Bloody Sunday families and reflecting on the terrible events of 50 years ago, not being distracted by the actions of a tiny minority who are determined to try and raise tensions”.
The Foyle MP continued: “The people who erected these flags speak for and represent nobody. Thankfully Derry is a city where people live side by side in peace and harmony and any right-thinking person will be appalled at the emergence of more of these flags in the lead up to such an important event in our shared history.”
Sinn Fein MLA Ciara Ferguson said: “There is huge upset in the city after British army Parachute Regiment flags were erected in Newbuildings and Drumahoe over recent days. This is a deliberate attempt to stir up tensions and hurt families”.
Alliance councillor Rachael Ferguson said: “I don’t doubt for one second the vast majority of people who live in these areas didn’t back the erection of these flags and political representatives from all quarters should condemn this. The lengths to which a small minority of people will go to raise tensions is deeply disappointing.”