One former British soldier - known only as soldier F - will be charged with the murder of civil rights demonstrators on Bloody Sunday.
The families later also called on the Attorney General to investigate whether Defence Secretary Gavin Williamson has interfered in the judicial process.
Speaking recently in a BBC interview, Mr Williamson said he was saddened that protection against “spurious prosecutions” would not be given to service personnel ahead of Thursday's decision.
John Kelly, whose 17-year-old brother Michael was killed, said the Attorney General should decide if Mr Williamson or other politicians had broken the law.
Mr Kelly said: “If they have, they should be charged.
“They cannot attempt to interfere in a judicial process just because they don’t like it, or because their voters don’t like it.”
Families and relatives of those who died marched through Londonderry ahead of an announcement.
Soldier F will face prosecution for the murders of James Wray and William McKinney and the attempted murders of Joseph Friel, Michael Quinn, Joe Mahon and Patrick O'Donnell.
Sixteen other veterans and two ex-members of the Official IRA, all of whom were investigated, learned on Thursday they will not face charges.
Thirteen civil rights demonstrators were shot dead on January 30 1972, on one of the most notorious days of the Northern Ireland Troubles.
Fifteen others were shot and injured. One of the injured died months later from an inoperable tumour and some consider him the 14th fatality.
Relatives of those who died expressed a mix of vindication, disappointment and defiance following the announcement.
While welcoming the news for the six families directly impacted by the decision to prosecute Soldier F – declaring that a “victory” – the campaigners said they would keep fighting for the other dead and injured.
ITV News Correspondent Peter Smith reacted to the Public Prosecution Service announcement:
Smith reported the families' disappointment as they learned of the single prosecution.
Ministry of Defence to fund the legal costs defending soldier F
Defence Secretary Gavin Williamson said the Ministry of Defence will pay the legal costs for soldier F.
"We are indebted to those soldiers who served with courage and distinction to bring peace to Northern Ireland," Mr Williamson said.
"The welfare of our former service personnel is of the utmost importance and we will offer full legal and pastoral support to the individual affected by today's decision. This includes funding all his legal costs and providing welfare support.
"The Ministry of Defence is working across Government to drive through a new package of safeguards to ensure our armed forces are not unfairly treated.
"And the Government will urgently reform the system for dealing with legacy issues. Our serving and former personnel cannot live in constant fear of prosecution."
The families of the victims reacted to the MoD funding announcement:
Bloody Sunday families left disappointed at single prosecution
Families of people killed on Bloody Sunday have said they are "not finished yet" at a press conference in the aftermath of the announcement.
As families of the victims gathered to give their reaction in Derry’s Guildhall, John Kelly, whose 17-year-old brother Michael was killed, said many had received a “terrible disappointment”.
But he welcomed the positive news for the six families impacted by the decision to prosecute soldier F.
“Their victory is our victory,” he said.
“We have walked a long journey since our fathers and brothers were brutally slaughtered on the streets of Derry on Bloody Sunday, over that passage of time all the parents of the deceased have died – we are here to take their place.”
Mr Kelly highlighted there were legal means of challenging the decisions not to prosecute.
“The Bloody Sunday families are not finished yet,” he said.
Mr Kelly heavily criticised Mr Williamson for his support for measures to potentially protect veterans from historic prosecutions, calling on the authorities to investigate whether his past remarks, and similar comments by other politicians, “broke the law”.
The solicitor for a number of the Bloody Sunday families, Ciaran Shiels, said: "We are disappointed that not all of those responsible are to face trial.
"We will give detailed consideration to the reasons provided for decisions not to prosecute the other soldiers, with a view to making further submissions to the Prosecution Service and we shall ultimately challenge in the High Court, by way of judicial review, any prosecutorial decision that does not withstand scrutiny."
But he hailed the news of the prosecution of soldier F as a "remarkable achievement by the families and victims of Bloody Sunday".
Mr Shiels said: "Notwithstanding the unprecedented attempted political interference with the independence of the judicial process, the families have not only succeeded in consigning the Widgery report to history, and securing the complete vindication and declaration of innocence of all of the victims of Bloody Sunday through the Saville Inquiry, they have now secured the prosecution of Soldier F for the murder and attempted murder of six innocent people."