DUP leader Ian Paisley has appealed for anyone who can help find the body of an IRA murder victim to come to him.
Mr Paisley and Mrs McVeigh met on Thursday
Mr Paisley was speaking before a meeting with Vera McVeigh, whose son Columba, 17, was kidnapped, murdered and secretly buried by the IRA in 1975.
He said he believed there were those who knew what had happened but were under pressure not to speak.
"Let's identify the body and let our dear sister and her family bring an end to it all," he said.
Earlier on Thursday, Sinn Fein President Gerry Adams said he was prepared to do everything humanly possible to help recover Columba's remains.
However, Mrs McVeigh said she was not impressed by Mr Adams' words.
Mrs McVeigh, who has recently been ill, added that the recovery of her son's body would mean the world to her.
Mr Paisley was contacted by the late Monsignor Denis Faul, a campaigner for the Disappeared, asking for his help.
In July, he said Fr Faul had told him not to give in until the families of the Disappeared had retrieved their loved ones' remains.
The meeting was set up by the DUP peer Lord Morrow.
Columba McVeigh's younger brother, Oliver, said that his mother talked about her murdered son every day, and needed closure.
He said that they hoped the involvement of the DUP leader would help his family and the other families of the Disappeared.
"They can certainly apply more pressure on Sinn Fein/IRA and on the two governments because there's going to be no closure for our families unless they turn up the bodies," he said.
"If anyone saw my mother - seen the state she was in, they would certainly want it to happen and I'm sure the other families would be the same."
In 2003, Mrs McVeigh said she had given up hope of ever finding her son's body.
She was speaking as police completed a 14-day excavation at bogland at Bragan near Emyvale, County Monaghan.
The operation was the third dig in the area and followed new information passed to the Irish government by the IRA.
In 1999, the IRA offered to help locate the bodies of the nine Disappeared. Three victims were found in 1999 while one was uncovered in 2003.