The Sinn Fein leader has been warned to take the threat seriously by the Police Service of Northern Ireland.
The threat on his life was made after his release from police questioning in relation to the 1972 murder of mother of 10, Jean McConville.
The police passed the message to the Adams' wife while he was not at home.
The 65-year-old had been questioned for four days over the McConville murder and links to the IRA.
Adams confirmed to Irish state broadcaster RTE: “The PSNI visited my home late on Sunday night and said that there was a serious threat to my life from what they described as criminals.”
Sinn Fein officials believe the credible threat was made by those opposed to the peace process.
Adams added: “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.”
Meanwhile Irish PM Enda Kenny has called on Northern Ireland’s Deputy First Minister Martin McGuinness to expand on comments made in relation to the Police Service of Northern Ireland.
McGuinness had claimed there is a ‘dark side’ operating within the PSNI and was critical of the decision to arrest Adams in the middle of campaigning for the European and local elections.
Kenny told reporters that he had spoken with British Prime Minister David Cameron, who confirmed there was no political interference in the arrest.
Kenny said: “If Martin McGuinness has evidence to prove otherwise he should contact the ombudsman’s office and lodge a formal complaint.”
In response, Sinn Fein leader Adams has moved to reaffirm his party's commitment to policing.
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.”