Sinn Féin claimed today dissident republicans were actively targeting Mr Gerry Adams.
West Belfast councillor Mr Michael Ferguson said today PSNI officers visited Mr Adams' home at about midnight last night and warned him that his life was in danger.
Mr Adams - who is currently on a political trip to the United States - was not at home, but the information was given to a family member.
Mr Ferguson said all threats of this nature had to be taken seriously, particularly at a time when the political process was in crisis."If this threat is true then I am sure that many republicans in west Belfast and further afield will be disappointed and indeed angry," he said.
"However, these republican micro-organisations operate without either a mandate or a strategy to achieve change or deliver a united Ireland.
"Sinn Fein are absolutely committed to the peace process and we will not be deflected by threats from loyalists, the British or indeed so called dissident republicans."
A PSNI spokesman refused to confirm or deny the claim, saying the force did not discuss the personal security of any individual.
"Where we believe that someone needs to review their personal security, we take steps to inform them," he said. "We never ignore anything that could put someone at risk."