"The appeal court will look at their file after the election," and if they find them to have links to Saddam's outlawed Baath party, "they will be eliminated", she said.
The blacklist - with more than 450 names and compiled by an integrity and accountability committee responsible for ensuring that individuals from the former regime do not take part - was widely criticised by Sunni political leaders who claimed it was being used as a political tool to marginalise them by the Shia-led government.
Washington had also expressed fear that any disputes could undermine the credibility of March 7 parliamentary elections.
Analysts also warned that the move could exclude Sunnis from politics and stoke sectarian tensions.
Jalal Talabani, Iraq's president, sought a compromise strategy by shifting the issue to the nation's highest appeals court, which then came up with a compromise of its own: the candidates could run, but would not be allowed to take office until their links to the former regime had been fully examined.
It was not clear, however, how many of the banned candidates would accept those rules. A prominent Sunni political figure on the list, Saleh al-Mutlaq, declined to give an immediate comment.
But al-Hussaini said the decision sets aside the election ban for now, but any winners on the list would "not enjoy their rights" until they have been cleared of any possible links to Saddam's regime.
Iraq's Shia-led government has pushed hard to weed out Saddam-era officials from public offices and security forces - a policy initiated by the United States shortly after the US-led invasion in 2003.
Many Sunnis believe the policy went too far, penalizing innocent people who had to join the Baath Party to advance in their chosen careers.
The elections scheduled for March comes at a critical juncture for Iraq, which is trying to put years of war that followed the 2003 US invasion behind it and revamp its economy by signing a raft of oil deals set to turn it into a top three oil producer.