She had faced a furious backlash from unionists and the SDLP after posting on social media.
She also said the pension would “discriminate, criminalise and exclude” those with paramilitary convictions.
The Foyle Assembly member and former MEP said in the tweet: “All victims should qualify for the pension.
“It reflects the Brit Gov policy & only its narrative of the conflict.
“It’s given legal protection to Brit armed forces who killed or injured or tortured Irish citizens during the conflict.
“NO to Discrimination Criminalisation Exclusion.”
She claimed it would mostly go to “those involved in collusion” and British troops, for instance paratroopers involved in shootings in Ballymurphy in west Belfast in 1971 and on Bloody Sunday in 1972.
The senior Sinn Féin member said the pensions were “mainly for those who fought Britain’s dirty war in Ireland”.
Ms Anderson later deleted the post from Twitter.
In an statement on Thursday morning, Ms Anderson said: “I apologise unreservedly for the hurt and offence caused by my tweet to people who suffered serious harm during the conflict here.
“My comments were clumsy were not directed at them and it was never my intention to cause them any hurt.”
— Martina Anderson Sinn Féin (@M_AndersonSF) August 26, 2020
Jennifer McNern, who lost lost both legs in an IRA bomb attack on the Abercorn Restaurant in 1972, said victims have campaigned for more than a decade for people who have been injured through no fault of their own.
“If you see the people who are applying for this pension – they are blind, they are paralysed and they are amputees,” she told the BBC.
“That is the people who will avail of this pension when it opens.”
There has been political disagreement over whether anyone convicted of inflicting serious harm during the Troubles should qualify for payments, and over who should fund the scheme.
Justice Minister Naomi Long has said the payments to the most badly hurt could cost £800 million (€888 million).
Sinn Féin Deputy First Minister Michelle O’Neill said: “As joint head of Government I remain committed to delivering a Victims Payment scheme, which is needs based and open to all who were seriously physically and psychologically injured during the conflict.”
Last week, Sinn Féin’s vice-president was highly criticised by the High Court for refusing to comply with a legislative requirement to set up the scheme to gain political leverage over the UK Government.
The joint legal challenge against the delay was brought by Jennifer McNern, who lost both legs in a Troubles bombing in 1972, and Brian Turley, one of the “Hooded Men” who were arrested and interrogated by the British army in 1971.
The scheme was due to open for applications at the end of May but little progress has been made due to a failure by the Executive Office (TEO) which is shared by Ms O’Neill and First Minister Arlene Foster, to nominate a Stormont department to take responsibility for it.
SDLP leader Colum Eastwood said: “The comments made by Martina Anderson this evening are unacceptable, disgusting and grossly insulting to hundreds of victims who sustained life-changing physical and psychological injuries related to Troubles incidents.”
DUP Foyle Assembly member Gary Middleton said the comments were deeply offensive.
“People who have lived most of their lives with shrapnel from an explosion in their body or who are haunted with the smell, taste and noise of a bombing should not be labelled by Martina Anderson.”
UUP justice spokesman Doug Beattie said it was “deluded nonsense”.
“Sinn Fein is clearly so committed to justifying the murderous criminality of the IRA which murdered and injured so many innocent people, that it is prepared to continue to slur its victims,” he said.
“They are without shame and demonstrate an appalling lack of humanity.”
