Ali Faisal, executive manager of the independent Debaathification Commission, said Sayid al-Hamashi was the object of a de-Baathification inquiry.
"His presence in this court violates the statutes ... and he must be replaced," he said.
He added that al-Hamashi's position at the court came to the commission's notice only when he was named by tribunal officials as taking over after the previous chief judge resigned last week.
Jaafar al-Mussawi, the chief prosecutor, however, dismissed the commission's comments and said court officials would want to see evidence before withdrawing support for al-Hamashi on the bench.
"Al-Hamashi denies having any relationship with the Baath party," al-Mussawi said. "The commission ... must provide its evidence to prove its credibility."
The commission, set up under US military rule after Saddam's overthrow in 2003, is charged with rooting out members of the Baath party from positions of power.
Faisal said the commission did not have to produce evidence but that those it accused of Baath membership could appeal through the courts.
The resignation of Kurdish chief judge Rizgar Amin, who has presided over the case since it opened in October, rocked a court whose ability to mount a fair trial had already been thrown into doubt by the killings of two defence lawyers and mutual accusations of intimidation.
Amin has made clear that he objected to political interference in the trial and court sources said on Wednesday it was looking increasingly unlikely that efforts would succeed to persuade him to stay on.
Al-Hamashi, a Shia and the most senior of the four other judges on the panel trying Saddam in the first case for crimes against humanity, was named by court officials on Monday as taking over temporarily, in accordance with standard procedure.
Sources inside the High Tribunal said he had also emerged as the consensus choice of his fellow judges to take over permanently in the event Amin stood by his resignation.
International human-rights groups have called for Saddam to be tried abroad, away from the climate of sectarian and ethnic tension that is dividing Saddam's once dominant fellow Sunni Arabs from the Shia and Kurds.
Amin resigned over political
interference in the trial
Allegations of Baath membership against judges and other tribunal officials troubled the US-sponsored court last year, before the first trial began, prompting several resignations.
Critics of Ahmad Chalabi, the deputy prime minister and a former favourite of Washington who fell out with US officials, accused him of pressing allegations of Baathist links after his nephew was ousted from his position in charge of the tribunal.
While support for Saddam is anathema in the new power structures, many Iraqi officials play down the relevance of past membership of the Baath party, saying many Iraqis joined simply to advance careers and played no active role in the movement.