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Adams said in a statement that he was "innocent of any part" in the death of McConville, a widowed mother of 10 who was abducted and murdered by the IRA in 1972, one of the most controversial crimes of Northern Ireland's sectarian violence.
"I believe that the killing of Jean McConville and the secret burial of her body was wrong and a grievous injustice to her and her family," said Adams, who has always denied membership of the Irish Republican Army, which admitted carrying out the murder.
McConville's body was found on a beach in the Republic of Ireland in 2003.
As the head of the political wing of the Irish Republican Army, Adams was for many the face of Irish militant nationalism during the IRA's bombing campaigns of the 1980s. British media were banned for years from broadcasting his voice.
Three decades of violence between Catholic militants seeking union with Ireland and mainly Protestant militants, who wanted to maintain Northern Ireland's position as a part of Britain, largely ended after a 1998 peace deal.
But investigations into historic crimes by pro-British militants were blamed by some observers for sparking some of the worst street violence for years in Northern Ireland in 2013.
It is unclear what affect the arrest might have on Northern Ireland's power-sharing government, whose deputy first minister, Martin McGuinness, is also a member of Sinn Fein.
A statement from the Police Service of Northern Ireland said a man had "presented himself" to police this evening, but it did not name the suspect.
Adams, who is the leader of Ireland's second largest opposition party, suggested his arrest could be politically motivated.
"I do have concerns in the middle of an election about the timing," he told Irish television station RTE before he volunteered himself for questioning.
Sinn Fein is campaigning for European elections on May 23.