The last episode of the three-part series is to air on January 24, just days before the Bloody Sunday anniversary.
Thirteen people died after members of the Parachute Regiment opened fire on civil rights demonstrators in Londonderry on January 30, 1972. A 14th victim died later in hospital.
The landmark Saville Inquiry concluded in 2010 that all those killed or injured were innocent.
Prime Minister David Cameron issued an official apology in the House of Commons, describing the killings as "unjustified and unjustifiable".
Foyle MLA Mark H Durkan said the decision to air the documentary in Northern Ireland was "unbelievably insensitive".
"Disgusted and dumbfounded that UTV are showing 'Paras: Men of War', glorifying the Parachute Regiment, on the cusp of the anniversary of Bloody Sunday when the Paras slaughtered 14 innocent people on the streets of Derry," he tweeted.
He called for the airing of the final episode of the documentary to be postponed until a later date.
An ITV spokesperson said that the documentary made no mention of Bloody Sunday and was not connected to other events in Northern Ireland.
"The three part series, The Paras: Men of War is an ITV commission, which is being shown on the ITV network, including UTV. The series is entirely contemporary, following young men going through the recruitment course now, charting their progress during the training and beyond," the spokesperson said.
"This series does not examine historical events and makes no mention of Bloody Sunday or other events in Northern Ireland.
"If any viewers were offended by the timing of the series, we apologise.”