Published Monday, 18 July 2011
It comes after a report by the Historical Enquiries Team (HET) found last month that the IRA was behind the shootings in the south Armagh village in 1976.
Ten men were forced at gunpoint to reveal their religion after their bus was hijacked as they went home from work, before being lined up and killed by 11 gunmen in one of the worst atrocities of the Troubles.
Relatives held two meetings on Monday - firstly with Owen Paterson at Stormont, then with Assistant Chief Constable Drew Harris at PSNI headquarters.
Mr Paterson told them he will not intervene in the matter.
In a statement he said he fully supported the right of every bereaved family during the Troubles to seek justice, but decisions on any evidence which could led to prosecutions is a matter for the police.
UUP Newry and Armagh MLA Danny Kennedy, who accompanied the delegation, said: "The Secretary of State believes that this is now a devolved matter but we contest that on the basis of duty of care and indeed of issues of national security which are still a responsibility of Owen Paterson and so this campaign will go on."
"There are questions as to the role of the British government at the time and particularly the Irish government, which allowed republicans to run rampant in south Armagh and use the republic as a safe area," he said.
Relatives say they presented police with a file containing information they say merits re-opening the case.
"Someone has to take responsibility for Kingsmills and what happened and it has never been done before. I think now is the appropriate time for that to be done," relative Karen Armstrong explained.
Last month, the HET found that the weapons used in the massacre could be linked to up to 100 other killings, included the murders of RUC Chief Superintendent Harold Breen and Superintendent Raymond Buchanan in South Armagh in 1989.
It said the motive for the attack was sectarian with each man murdered because he was a Protestant.
The report also listed failings by the small 12-man RUC team that investigated the killings, detailing how they failed to trace and interview a number of potential witnesses.
Police say they will meet relatives again in six weeks time.