Mrs Foster was speaking while surrounded by relatives of the deceased as they prepared to attend another day’s hearings in the legacy inquest into the matter in Belfast.
Ten Protestant workmen were shot by 11 IRA men at Kingsmills in south Armagh as they returned home from work in January 1976.
In March 2015 Mr Kenny met the families in Bessbrook where he promised full transparency with Garda files on the attack, which was largely executed from the south.
Mrs Foster said that after meeting the families there was “disappointment of course that they haven’t received the information from the Republic of Ireland that they have asked for, that the coroner has asked for ... despite the fact that promises were made that there would be full and open transparency”.
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Asked if Mr Kenny’s promises would vanish with his imminent exit from office, Mrs Foster replied: “Well we are certainly continuing to push this issue, as I have done during the talks with [Minister] Charlie Flanagan.”
She added: “But...whoever is going to lead the new government, I will seek a meeting with that person.”
Asked how she would feel if the southern files were released, 89-year-old Bea Worton, whose son Kenneth was one of those killed, said: “Well we would know where we were then. They don’t seem to tell us nothing at all.”
Later, former RUC constable Derek Burnett Smith, who attended the shooting scene, told the inquest he saw the bodies lying in the road and there were “large pools ... with heavily congealed blood” on the tarmac which contained bullet fragments and “some brain tissue”.
The hearing was adjourned for a time as some relatives had to leave the court due to the graphic details.
Mr Smith saw seven bodies lying on the road, four at the rear of the minibus and three between the minibus and the ditch.
He confirmed that one gunman armed with a Sten sub machine gun had managed to hit eight of the 10 victims.
Ex-forensic officer Jacynth Hamill said it had been impossible to run gunshot residue tests on most of the victims’ clothes because they were “saturated with blood”. Almost all their clothes “had bullet holes in the backs”.
She was able to say that the victims had been shot at close range in the back from a range of less than three feet.