Taoiseach challenges Adams over 'Price Tapes'
Meanwhile, US Secretary of State John Kerry has been warned that the stability of the Northern Ireland peace process could be undermined if interview material from the Boston College archive is released.
The remarks come just days after recordings of secret interviews with the late IRA bomber Dolours Price were handed over to police in the North, who are investigating the disappearance of Ms McConville. Police Service of Northern Ireland (PSNI) officers travelled to the US to collect the tapes from the US Justice Department, after they had been secured by subpoena from Boston College.
Before her death, Ms Price publicly alleged that Mr Adams was an IRA commander who ordered Ms McConville's kidnapping and killing.
Mr Adams has consistently rejected the accusations. In the Dail Mr Kenny told Mr Adams that for "one reason or another" his name was always associated with "elements of that".
"There's a challenge for you now," Mr Kenny said. "Say it on the record."
Meanwhile Senator Robert Menendez, chairperson of the US Senate Foreign Relations Committee, wrote to Mr Kerry about the matter. He warned release of recordings could "still have the effect of threatening the precious peace won by the Good Friday Agreement".
Boston College researchers had fought attempts by the PSNI to secure the recordings and have maintained they do not include Ms Price making allegations that Mr Adams ordered Ms McConville's kidnapping.
A US appeals court ruling limited the tapes that could be released to those relating to her murder. A spokesman for Boston College said it was still in possession of other tapes sought in a second subpoena and had several more weeks to consider its legal options in relation to those.
Mr Kenny later called on anyone with information on the whereabouts of the bodies of the "Disappeared" to come forward as "a matter of common, human decency." He was speaking after he met a group of family members at Leinster House whose loved ones were murdered and buried in secret during the Troubles.
He also met Frank Murray of the Independent Commission for the Location of Victims' Remains, and was updated on their ongoing work to recover the remains of the seven victims who are still missing.