On Sunday relatives of the 14 people killed and 12 injured on Bloody Sunday called for all those responsible to be prosecuted.
Citing sufficient evidence and public interest in court proceedings, lawyers for the families affected by the shootings in Derry said the prosecutions should go ahead.
The call came as thousands of people took part in what some press reports called one of the last marches to commemorate the 1972 shootings.
Last year the Saville Report exonerated all 14 people killed by British Paratroopers, who opened fire without warning on a civil rights march on Bloody Sunday, January 30, 1972.
A spokesman for Madden and Finucane Solicitors, one of the legal groups taking the case, told the press: "Following careful consideration of Lord Saville's report and its implications, we have submitted detailed representations to the Public Prosecution Service requesting that those responsible for the murders and attempted murders on Bloody Sunday be prosecuted in court."
"It is clear to us that the evidential and public interest tests for bringing prosecutions have been satisfied."
The spokesperson added: "Our submissions have also been forwarded to the Crown Prosecution Service in England in respect of the perjury committed by the soldiers when giving their evidence to the tribunal whilst in London."
The 5,000-page Saville Report was built on the testimony of 921 witnesses and 60 volumes of written evidence.
None of the witnesses was granted blanket immunity from prosecution, but all were immune from prosecution on the grounds of self-incrimination. (There there was no immunity for perjury.) Evidence given by the witnesses can not be used against them in any future legal proceedings.