Speaking at a press conference after four days of questioning about the killing of the Belfast mother-of-ten, Mr Adams said he was "concerned about the timing" of his detention ahead of "a very important European election and local government elections across the island of Ireland."
He also criticised the fact that he was detained under the Terrorism Act when he presented himself at Antrim Serious Crime Suite on Wednesday evening after the PSNI contacted his solicitor.
"I want to make it clear that I support the PSNI," he said.
"I will continue to work with others to build a genuinely civic policing service."
However, he said he felt those who authorised his arrest and detention "could have done it differently" and sent out the "wrong signal".
He explained that the PSNI made 33 taped interviews during his time in custody.
Surrounded by senior Sinn Féin figures, he told reporters the allegations of his involvement in the McConville case, which he rejects, are based "almost exclusively on hearsay from unnamed alleged Boston College interviewees but mostly from Dolours Price and Brendan Hughes".
The recent police activity followed a decision by a US court compelling a Boston university to hand over to the PSNI recorded interviews about the case.
"I reject all the allegations, and rejected all the allegations made against me in these tapes," Mr Adams said.
Let me very clear - I am innocent of any involvement in any conspiracy to abduct, kill or bury Mrs McConville.
Sinn Féin president Gerry Adams
Mrs McConville was kidnapped by the IRA, interrogated, shot in the back of the head and then secretly buried over 40 years ago - becoming one of the so-called "Disappeared" victims of the Troubles. She was wrongly suspected of being an informer for the British Army.
The body of the 37-year-old widow was not found until 2003 on a beach in Co Louth.
One of her sons has now called for an independent investigation by a team from outside Northern Ireland.
"I am conscious that there is another family at the heart of all of this and that is the family of Jean McConville," Mr Adams said on Sunday night.
"I have worked hard with others to have this injustice redressed and for the return of the bodies of others killed during the conflict and secretly buried by the IRA, and I will continue to do so."
He said the allegations were part of a "sustained, malicious, untruthful and sinister campaign" against him.
Earlier Mr Adams left via the back entrance of Antrim police station, two hours after he was formally released pending a report to the Public Prosecution Service.
The delay came after a number of loyalist protestors blocked the entrance of the station amid a heavy police presence.
We would like to see all the investigations taken out of Northern Ireland, we would like an independent body to do this so there is no political pressure on the police.
The decision on whether to proceed with a prosecution now rests with the deputy director of Public Prosecutions Pamela Atchison after it emerged that the Director of Public Prosecutions Barra McGrory QC previously acted as Mr Adams' lawyer.
A spokeswoman for the PPS confirmed Mr McGrory would have no decision-making role in the case.
"No prosecutorial decision will be taken by the director Barra McGrory QC in this case," she said.
Before Mr Adams' release on Sunday, Sinn Féin MLA Gerry Kelly was granted access into the police station and spoke with the former west Belfast MP.
He said Mr Adams was "doing fine" but had concerns about the impact his arrest will have on the PSNI's image.
"He's worried about the damage it might be doing to the image of policing and that it's being mishandled in that type of fashion."
The MLA confirmed that during questioning, officers used "open source material" - including the Boston College tapes as well as old pictures, newspaper articles and books.
What we need in these circumstances is leadership - it is patently absent in the republican movement.
DUP leader Peter Robinson
The arrest of Mr Adams triggered a political row at Stormont after Deputy First Minister Martin McGuinness said it was a "political" move by an "embittered rump of the old RUC" within the PSNI.
At a rally organised in West Belfast in support of the party leader on Saturday, he also accused police of "deliberately and cynically exploiting the awful killing of Jean McConville and the grief and hurt of her family."
First Minister Peter Robinson later hit out at Sinn Féin over what he called the party's "unacceptable" attempt to blackmail the PSNI following the arrest.
The DUP leader criticised what he called "republican bullyboy tactics" and an "obscene politicising of the policing process".
"The publicly conveyed threat to the PSNI delivered by the highest levels of Sinn Féin that they will reassess their attitude to policing if Gerry Adams is charged is a despicable, thuggish attempt to blackmail the PSNI," he said.
"I warn Sinn Féin that they have crossed the line and should immediately cease this destructive behaviour."
Justice Minister David Ford and Northern Ireland Secretary Theresa Villiers have also defended the police's handling of the arrest and denied it was politically motivated.