Some Labour MPs had been calling for Abbott to be readmitted to Labour and more than 38,000 people had signed a petition backing her return.
Earlier, following reports in the Sun newspaper, external about Abbott’s possible readmission, Jewish groups expressed concern.
The Board of Deputies said: “This is an early test of resolve for the Burnham administration.
“It is hard to conceive of the whip being restored unless there is clear and sustained evidence of genuine remorse, a proper understanding of why those comments were so hurtful, and an unequivocal recognition that antisemitism is racism.
“While people can learn from their mistakes, Diane Abbott’s past record is not encouraging in this regard.”
The Jewish Leadership Council said the prime minister “must explain how returning that whip to Diane Abbott is consistent with this zero tolerance approach to antisemitism.”
Following the party’s decision to accept Abbott and Reid back into the parliamentary party, two MPs remain suspended from Labour.
Karl Turner was suspended in March for making “uncollegiate” comments about colleagues, BBC News understands.
However, Turner said it was “clear” his suspension was due to his criticism of the government’s policy on jury trials.
Dan Norris, the MP for North East Somerset and Hanham, was suspended after being arrested on suspicion of sexual offences.
