Published Monday, 05 May 2014
The party said Mr Adams' home was visited by police. (© UTV)
A statement on Monday afternoon claimed police visited his home on Sunday evening to warn him of a "serious threat from criminal elements".
It added that officers also notified party member Bobby Storey of a similar threat.
Mr Adams was on Sunday released pending report to the PPS by police investigating the 1972 abduction and murder of Jean McConville. He has always denied any involvement.
Mr Storey recently addressed a crowd at the unveiling of a mural in support of Mr Adams.
Speaking about the threat, Mr Adams told CNN: "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."
Raymond McCartney of Sinn Féin said: "I can confirm that the PSNI visited the homes of Gerry Adams and Bobby Storey last night to warn them of a credible threat against their lives
"The PSNI officer told Gerry Adams wife Collette that they had information of a "serious threat from criminals" to Gerry Adams who was not at home at the time.
"Clearly there are elements that are opposed to the peace process and anti-Sinn Féin. We will not allow them to succeed nor will we be deflected from our determination to build the peace process."
A spokesperson for the PSNI said: "We do not discuss the security of any individual.
"However, if we receive information that a person's life may be at risk we will inform the relevant persons accordingly. We never ignore anything which may put an individual at risk.
"No inference should be drawn from this."
© UTV News