The Nets suspended Irving without pay for at least five games after he promoted an antisemitic film on social media.
The team said in a statement that Irving's refusal to state he is not antisemitic is detrimental to the team.
The Nets did not say what steps Irving would have to take in order to get back on the floor.
Irving pledged $500,000 to the Anti-Defamation League on Wednesday, stating he takes responsibility for the negative impact of his post towards the Jewish community, but he hasn't apologized.
He is currently not fit to be associated with the Brooklyn Nets.
A film called "Hebrews to Negroes: Wake Up Black America" contains antisemitic quotes and was linked to by Irving. Many NBA watchers called on Irving to be suspended for his role in the controversy. NBA Commissioner Adam Silver called Irving's comments reckless and criticized the player for failing to apologize. The seven-time all-star guard has a history of pushing conspiracy theories and sat out most of last season after not getting the vaccine.
The NBA Commissioner criticized Irving for not offering an unqualified apology.
There is controversy over antisemitism and the latest to call it out is the Nets star.