In December, families handed in a petition to Downing street calling for an independent investigation into the killings.
John Teggart, whose father Danny died, said the families wanted a panel to look into the shootings.
He said an international figure could head the panel.
“It’s 40 years since my father was murdered in Ballymurphy. There’s been no police investigation. It needs to be independent. It needs to be done by the right people, in agreement with the families.
“To sort out and start talking about terms of reference we need to be sitting with the man who holds the power, that’s David Cameron.”
He said Ballymurphy could have been dealt with during the Saville Inquiry into Bloody Sunday.
The families have previously called for an independent inquiry into the killings.
The victims, which included a priest and a mother-of-eight, were killed over the course of three days in August 1971 by members of the Parachute Regiment during Operation Demetrius, when people suspected of paramilitary activity were interned.
The Army said it opened fire in the Ballymurphy area in response to gunfire from republican paramilitaries.
Last November, the Attorney General John Larkin announced that new inquests would be held into their deaths.
The families said the decision by Mr Larkin was an important step in their ongoing campaign for justice but said their campaign for an independent investigation would continue.
The Northern Ireland Office has ruled out any public inquiry into the killings akin to the Bloody Sunday Tribunal.
The 10 people shot dead
- Fr Hugh Mullan
- Francis Quinn
- Daniel Teggart
- Joan Connolly
- Joseph Murphy
- Noel Phillips
- Edward Doherty
- John Laverty
- Joseph Corr
- John McKerr
Army shooting inquests welcomed 15 NOVEMBER 2011, NORTHERN IRELAND
Ballymurphy group meet Robinson 18 FEBRUARY 2011, NORTHERN IRELAND
Victims’ families lobby parties 16 NOVEMBER 2010, NORTHERN IRELAND
Church to report on 1971 killings 29 JULY 2010, NORTHERN IRELAND
MP calls for Ballymurphy inquiry 08 DECEMBER 2010, NORTHERN IRELAND
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