Labour's chief whip has asked ex-party leader Jeremy Corbyn to "unequivocally" apologise for saying the scale of anti-Semitism in the party had been "overstated for political reasons".
Mr Corbyn was suspended from the party following his comments but later readmitted as a member after saying he regretted any "pain" caused.
But, Sir Keir Starmer blocked Mr Corbyn from returning as a Labour MP.
The Labour leader said he would keep the decision under review.
The row between the former and current leader was triggered when the Equalities and Human Rights Commission (EHRC) published a report, saying Labour had broken the law over its handling of anti-Jewish racism complaints by party members .
In a letter to his former boss, Nick Brown, Labour's chief whip, said Mr Corbyn's response to the report caused "distress and pain" to the Jewish community.
The chief whip is responsible for organising a party's MPs in Parliament so they vote the way the party wants them to, and can discipline any who do not follow the party line.
Mr Brown asked the Islington North MP to "unequivocally, unambiguously and without reservation apologise for your comments".
He also sought confirmation that Mr Corbyn would remove or edit his response on Facebook - and that he would cooperate fully with the party's efforts to implement the EHRC's recommendations.
The tone of Nick Brown's letter suggests that without making an unequivocal apology, Mr Corbyn is unlikely to have the Labour whip restored.
But allies of Mr Corbyn have accused the current Labour leader of acting in bad faith.
They claim an agreement was reached with party officials and members of Sir Keir's staff that would have seen Mr Corbyn readmitted without an apology.
They now fear his suspension could be indefinite, and that the dispute between a former and current leader will end up in the courts.
Labour sources deny that any such deal was reached.
Following publication of the EHRC report in October Mr Corbyn said he was "always determined to eliminate all forms of racism" and insisted his team had "acted to speed up" the complaints process.
He also said the scale of anti-Semitism within Labour had been "dramatically overstated for political reasons by our opponents inside and outside the party".
His comments prompted the party to suspend its former leader.
Three weeks later Mr Corbyn sought to clarify his words saying: "To be clear, concerns about anti-Semitism are neither 'exaggerated' nor 'overstated'.
"The point I wished to make was that the vast majority of Labour Party members were and remain committed anti-racists deeply opposed to anti-Semitism."
He was subsequently readmitted to the party as a member; however Sir Keir did not allow him back into the Parliamentary Labour Party - a decision Mr Corbyn's lawyers have challenged.