Sinn Féin has said party president Gerry Adams has been warned of a "credible" death threat.
The party blamed those opposed to the peace process for the message, which it said was passed by police to Mr Adams' wife while he was not at home.
Mr Adams tonight told CNN's Christiane Amanpour: "The PSNI visited my home late last night and said that there was a serious threat to my life from what they described as criminals.
"That's the risk that I and others have to take, and are prepared to take, because the peace process is bigger than us.
"This is why we have to be very steadfast and resolute and patient as well."
Mr Adams, 65, was released from Antrim police station after four days of questioning about the 1972 killing of mother-of-ten Jean McConville and other alleged links with the IRA.
A file is being prepared for the Public Prosecution Service in Northern Ireland.
Mr Adams denies any involvement in the murder and abduction.
The Sinn Féin leader and several high-profile party members criticised the timing of the arrest, as it came during campaigning for the Local and European Elections.
Taoiseach Enda Kenny tonight said Martin McGuinness should lodge a formal complaint if he feels that there is a "dark side" operating in the PSNI.
Mr McGuiness has claimed that the arrest was a deliberate attempt to influence the elections.
Speaking in Mullingar, Mr Kenny said he had spoken with British Prime Minister David Cameron, who he said confirmed there was no political interference in the arrest.
Mr Kenny said that if Mr McGuinness has evidence to prove otherwise he should contact the ombudsman’s office and lodge a formal complaint.
Sinn Féin previously accused an "anti-peace process rump" within the PSNI of orchestrating the detention with the aim of damaging the party.
This was angrily rejected by political rivals, including DUP leader and First Minister Peter Robinson.
However, Mr Adams last night moved to dispel any suggestion that Sinn Féin's commitment to policing had wavered in the wake of the affair.
He said: "I want to make it clear that I support the PSNI. I will continue to work with others to build a genuinely civic policing service.
"The old guard which is against change - whether in the PSNI leadership, within elements of unionism, or the far fringes of self proclaimed but pseudo republicans - they can't win."
Earlier, Secretary of State for Northern Ireland Teresa Villiers said it would have been very destabilising if Sinn Féin had withdrawn its support for the PSNI following the arrest of Mr Adams.
Speaking on RTÉ's Morning Ireland, Ms Villiers said both the British and Irish governments had been in close contact in recent days while Mr Adams was in custody.
She said she had spoken to Tánaiste Eamon Gilmore on several occasions.
Mr Kenny and Mr Cameron also spoke yesterday to discuss the situation surrounding Mr Adams's arrest.
Ms Villiers said: "Both governments would share my view that it is very important for, regardless of the outcome of the case, the Northern Ireland political parties to continue to work to make sure the devolved institutions operate effectively.
"It would have been very destabilising if Sinn Féin had withdrawn their support for the police, and policing and justice. I welcome very much that they have not done that."
McConvilles warned of backlash by Adams
Mrs McConville's son Michael has said Mr Adams warned of a "backlash" when he told the Sinn Féin leader he would release the names of those involved.
Mr McConville said the "threat" was made around the time the report being drawn up by Northern Ireland's former police ombudsman Nuala O'Loan into claims that his mother was an informer was close to being finalised.
Mr Adams had brokered a series of meetings between Mr McConville and members of the IRA.
"I asked the IRA if Nuala O'Loan came out and made her statement clear that my mother wasn't an informant would they come out and apologise for the murder of our mother and they turned around and says 'no they won't' and they'd be making a statement saying that 'your mother was an informant'," Mr McConville told BBC Radio 4's Today programme.
"I says to them 'well, if that's the case I'll be releasing the names into the public for the people that came and took our mother that night'.
"When I was having these meetings Gerry Adams used to get the meetings called."
Mr McConville said he used to tell Mr Adams what had happened in the meetings and warned him that he would release the names of those involved if Ms O'Loan's report was disputed.
He added: "Gerry Adams says to me 'Michael, you are getting a letter of support from the Republican people'. He says 'if you release the names I hope you are ready for the backlash'.
"I took it as a threat."
Mr McConville said that "could" have meant a backlash against the peace process, but said he took it to mean the "backlash from Republican people".
"We are calling for this case to be taken out of Northern Ireland and an independent body to look at it so the McConville family gets justice for its mother because we don't think we can get justice for our mother the way things are happening in this country."
Mr McConville said he was "disappointed" that Mr Adams had been released.
He said: "We thought we were going to get Gerry Adams brought to court."
Mr Adams this evening denied threatening Mr McConville.
Speaking on CNN, he said: "First of all I never said that. I have tried my best...
"I can understand absolutely, given what Republicans have done to their family and their mother, I can understand absolutely why the McConville family feel the way that they feel, so let me say that as a matter of record.
"But I am very, very clear - and they may reject this - I have been trying my best to support and help all of the victims, but I have a particular wish to help the victims of the IRA."
Gilmore calls for progress on talks
Elsewhere, Mr Gilmore has said he believes there is a window of opportunity in which progress could be made in negotiations among Northern Ireland's politicians.
Speaking on RTÉ's News At One, the Tánaiste said last year's talks chaired by Dr Richard Haass had not failed.
He said they could be concluded if the parties wanted to address the legacy of the past.
The Haass talks broke down on New Year's Eve without a consensus being reached.
They had examined the disputes on flags, parades and the legacy of the Troubles.
Mr Gilmore said he will be in contact with Mr Haass today to update him on the latest developments.
He said he believed there was time between the elections in May and the marching season in July to make progress on some issues.
The Tánaiste also rejected claims that the Government has taken a "hands-off" approach to Northern Ireland. He said his office has been very active on the issue.