Dissident republicans have strongly denied they have plans to kill Mr Gerry dams. Both the "Real IRA" and Continuity IRA sources described the eports as "complete and absolute nonsense".
There was "no threat whatsoever" to the Sinn Féin president's life, they said. Sinn Féin said Mr Adams had been told by police that intelligence reports suggested he was being actively targeted by dissident republicans.
Speaking yesterday, Mr Adams said he would not be deflected from the peace process but he was taking the threat seriously.
"Some of these groups are so heavily infiltrated that it is very hard to know who is pulling the strings or indeed if there is a real threat. All I know is I have a job of work to do, that I was elected to represent people," he said.
"I don't intent to be intimidated from representing those who support our party and that wider group of people who support the peace process."
The Police Service of Northern Ireland would not confirm the details, but a spokesman said: "Where we believe that someone needs to review their personal security, we take steps to inform them. We never ignore anything that could put someone at risk."
It is understood the development is linked to an alleged "Real IRA" spy ring which was uncovered at the Royal Victoria Hospital in Belfast two months ago. Medical records of politicians, prison officers and others had reportedly been copied by dissident republicans.
However, a "Real IRA" source denied the Sinn Féin president was being targeted.
"This is a load of rubbish. Gerry Adams is not in any danger. We have never been interested in targeting Sinn Féin and Provisional IRA members.
"The violence and aggression has always been directed from them against us." The "Real IRA" accused the police of "stirring".
A spokeswoman for the 32 County Sovereignty Movement said the situation was "so ludicrous" that the mother and brother of west Belfast "Real IRA" commander Joe O'Connor, who was shot dead by the Provisional IRA three years ago, had been told their personal details were in the hands of the "Real IRA".
A Continuity IRA source said his organisation presented no threat to Mr Adams' life. Sinn Féin said police visited Mr Adams' home on Friday night to tell him about the threat.
Mr Adams was not at home but the information was given to a family member.
Sinn Féin councillor Mr Michael Ferguson said: "It is something which isn't very pleasant to be told, but Gerry remains committed to the peace process, as does Sinn Féin.
"If this threat is true, then I am sure many republicans in west Belfast and further afield will be disappointed and indeed angry at anybody contemplating such a thing.
"These republican micro-organisations operate without either a mandate or a strategy to achieve change or deliver a united Ireland. Sinn Féin is absolutely committed to the peace process and we will not be deflected by threats from loyalists, the British, or indeed so-called dissident republicans."
The "Real IRA" and Continuity IRA are opposed to the peace process and the Belfast Agreement, which they claim cements partition. Recent attempted bombings by the groups have been thwarted by the security forces.
The Provisional IRA has abducted and beaten up several dissidents over the years. After Joe O'Connor's murder, there were fears of a feud between the "Real IRA" and the Provisional IRA. However, despite continuing tensions, this has been avoided.