Sinn Féin leader Gerry Adams continues to be questioned by Northern Ireland police in connection with the 1972 murder of Jean McConville.
Mr Adams has spent the night in custody after going to Antrim police station, where he was arrested.
Speaking before his detention on Wednesday evening, Mr Adams said he was "innocent of any part" in the murder.
Mrs McConville, a 37-year-old widow and mother-of-10, was abducted and shot by the IRA.
Her body was recovered from a beach in County Louth in 2003.
Police said a 65-year-old man presented himself to officers at Antrim police station and was arrested.
In a statement, Sinn Féin said: "Last month Gerry Adams said he was available to meet the PSNI about the Jean McConville case. That meeting is taking place this evening."
Mr Adams added: "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.
"Well publicised, malicious allegations have been made against me. I reject these.
"While I have never disassociated myself from the IRA and I never will, I am innocent of any part in the abduction, killing or burial of Mrs McConville."
His party colleague Alex Maskey condemned the timing of the arrest, just over three weeks from the European and local government elections.
However, Mrs McConville's son Michael, who was 11 when his mother was murdered, welcomed the arrest.
"We're just happy to see everything moving as it is moving at the minute," Mr McConville said.
"Me and the rest of my brothers and sisters are just glad to see the PSNI doing their job. We didn't think it would ever take place [Mr Adams' arrest], but we are quite glad that it is taking place.
"All we're looking for is justice for our mother. Our mother, on the seventh of next month, would have been 80 years of age.
"Although we didn't spend much time with our mother, we'd have like to have spent a lot of time with her. If the IRA hadn't have killed our mother, God knows, she still might have been alive today."
Mr McConville said what he really wanted was for the perpetrators to be tried as "war criminals" at the international court in the Hague, rather than being brought before courts in Northern Ireland.
Northern Ireland's First Minister Peter Robinson said he "commends the police for the action they have taken".
Speaking to the media on Thursday, he said: "It strengthens our political process in Northern Ireland for people to know that no one is above the law, everyone is equal under the law and everyone is equally subject to the law."
Prime Minister David Cameron said there had been "absolutely no political interference in this issue".
Taoiseach (Irish prime minister) Enda Kenny also rejected suggestions from senior Sinn Féin figures that the arrest of Mr Adams had been politically motivated.
"This is still a live murder case, this is still a live investigation," he said.
"All I can say is that I hope the president of Sinn Féin answers in the best way he can, to the fullest extent that he can, questions that are being asked about a live murder investigation."
Mrs McConville, one of Northern Ireland's Disappeared, was kidnapped in front of her children after being wrongly accused of being an informer.
The claim that she was an informer was dismissed after an official investigation by the Northern Ireland Police Ombudsman.
Mrs McConville was held at one or more houses before being shot and buried in secret.
The Disappeared are those who were abducted, murdered and secretly buried by republicans during the Troubles.
The IRA admitted in 1999 that it murdered and buried at secret locations nine of the Disappeared.
The Independent Commission for the Location of Victims' Remains was established in 1999 by a treaty between the British and Irish governments.
It lists 16 people as "disappeared". Despite extensive searches, the remains of seven of them have not been found.
On its website, the commission said all information it received was privileged - it can not be passed on to other agencies or used in a court of law. It can only be used to try and locate the remains of the Disappeared.
Jean McConville's remains were found in 2003 by a man walking at Shelling Hill beach, near Carlingford.
It is understood that because Mrs McConville's body was found by accident by a member of the public rather than through information given to the commission, a criminal investigation can take place.
Last month, Ivor Bell, 77, a leader in the Provisional IRA in the 1970s, was charged with aiding and abetting the murder.
There have also been a number of other arrests over the murder recently.
The case against Bell is based on an interview he allegedly gave to researchers at Boston College in the US.
The Boston College tapes are a series of candid, confessional interviews with former loyalist and republican paramilitaries, designed to be an oral history of the Troubles.
The paramilitaries were told the tapes would only be made public after their deaths.
However, after a series of court cases in the United States, some of the content has been handed over to the authorities.
Mr Adams has never been charged with membership of the IRA. He was, however, interned in 1972 under the controversial Special Powers Act, but briefly released in order that he could take part in talks in London between representatives of Sinn Fein and the then Home Secretary Willie Whitelaw.
He was later re-arrested and interned at Long Kesh. Following an aborted escape attempt he received a prison sentence.