Sinn Féin MLA Ciara Ferguson said the erection of flags is a deliberate attempt to cause hurt to the Bloody Sunday families.
She said: “There is huge upset in the city after British army Parachute Regiment flags were erected in Newbuildings and Drumahoe over recent days.
“Given this British regiment's brutal history in Derry, this is a deliberate attempt to stir up tensions and hurt families ahead of the 50th anniversary of Bloody Sunday and the murder of 14 civilians by the British Army in Derry."
The Foyle MLA called for the political leadership and the removal of the flags.
“I have stood with those families in recent days, they are steadfast, courageous and determined in their campaign for truth and justice for their loved ones.
“I am calling on all political parties and community leaders to condemn the erecting of these flags and to use their influence to have them removed immediately," she said.
SDLP MLA Sinéad McLaughlin said: "The emergence of Parachute Regiment flags in parts of Derry in the run up to the 50th anniversary of Bloody Sunday is both distressing and disheartening.
"They can only have been erected to cause hurt to the victims and survivors of Bloody Sunday and their families and I would ask those who put them up to show some decency and remove them immediately.
“I know the people who erected these flags do not speak for these communities. The vast majority of the people in our city just want to get along with their neighbours in an atmosphere of mutual respect and understanding.
“Bloody Sunday was one of the worst atrocities of our troubled past and its anniversary will bring back painful memories and pause to people right across these islands. We should be using the 50th anniversary to remember those who died and to think about how far we’ve come as a society since 1972.”