Mr Adams has repeatedly denied being a member of the IRA, despite repeated accusations from the Government and former Provos.
Most recently, he was implicated in the murder of Belfast mother-of-10 Jean McConville.
CNN's World Report carried an interview with Mr Adams, in which he was described as "a former IRA paramilitary commander".
A leading Fine Gael councillor has called on Mr Adams to "treat the Irish people with respect and come clean about his past".
Fine Gael's leader of Limerick City Council, Diarmuid Scully, said the report has gone out around the world.
"If Gerry Adams is willing to be described as such in the international media, why does he continue to deny his former IRA membership here in Ireland. Surely the people deserve to know the truth about those who represent them," he said.
Sinn Fein said Mr Adams's spokesman has complained to CNN's representative in Belfast about the description of the party president. In the report on the loyalist violence and flags protest in Belfast, Mr Adams was described as "a former IRA paramilitary commander" and also as "the leading Catholic politician in Northern Ireland".
Mr Adams was speaking out against the ongoing violence in Belfast at a peace vigil at the weekend.
He continues to be routinely accused of being an IRA leader and member of the Army Council. Taoiseach Enda Kenny has joined in the statements declaring Mr Adams as a member of the IRA.
Last year, convicted IRA bomber Dolours Price accused Mr Adams of having a leading role in the Provos, including personal involvement in the murder of Jean McConville.