Foyle Sinn Féin MLA has said she is "disgusted" by what she described as republicans exploiting the grief of the families of the hunger strikers to attack her party.
Ms Anderson made her remarks during the annual Derry Volunteers Commemoration event in the City Cemetery on Sunday.
A crowd of up to 1,000 local republicans took part in the march from the Creggan shops to the republican monument in the City Cemetery.
Her comments come amid claims by former blanketman Richard O'Rawe that the deaths of six of the hunger strikers could have been prevented after a deal, which he claims was accepted by the IRA's jail leadership was rejected by the organisation's overall leadership.
The claim has been supported by the IRSP and several former prisoners who were in Long Kesh at the time but has been flatly rejected by Sinn Fin.
The families of most of the hunger strikers, including County Derry man, Kevin Lynch, issued a statement last week calling for an end to the controversy.
Speaking at Sunday's commemoration, Ms Anderson said: "I am disgusted that so many republicans are exploiting the grief of the families to attack us.
"In doing so they have got into bed with the right wing press.
"They should be ashamed of themselves.
"If they have any honour at all they will call a halt to their shameful actions."
Memory of the dead
The Foyle MLA also said Sinn Fin are continually motivated by the memory of dead IRA volunteers and added that the current political situation could not have been achieved without their efforts.
"Today republicans are wielding unprecedented political power in Ireland.
"It is the volunteer soldiers of the IRA who made all that possible," she said.
At the commemoration, the Roll of Honour was read by Tiernan Heaney, nephew of IRA member Denis Heaney, and the Roll of Remembrance was read by Aoife McNaught of gra Shinn Fin. Wreaths were laid on behalf of Sinn Fin, the Republican Graves Association, gra Sinn Fin, and glaigh na h'ireann.
The National Anthem was sung by Sara Griffin.