Speaking to reporters after his release, Adams claimed his innocence and blamed the arrest on "old guard using the old methods."
"They didn’t have to use pernicious coercive legislation to deal with a legacy issue, even one as serious as this which I was voluntarily prepared to deal with. They didn’t have to do it in the middle of an election campaign," he said.
Adams has served as president of the Sinn Fein political party, once considered the political arm of the IRA, since 1983. He never admitted publicly to membership in the IRA, but has long been accused of serving as the organization's commander in Belfast.
McConville, 37, was wrongly accused of spying for the British during a decades-long conflict, the Troubles, between Protestants loyal to the United Kingdom and Catholics who supported reunification with Ireland.
The widowed mother of 10 was abducted in front of her children and shot once in the back of the head. Her body wasn't found until 2003.
Despite the arrest, Adams reiterated his commitment to peace on Sunday.
"The IRA is gone, it's finished," he said. "I want to make it clear that I support the PSNI."
Police have handed evidence over to the Northern Ireland Public Prosecution Service, which will decide if there is enough to pursue charges against Adams.