Irving sparked outrage by tweeting a link to a film that contains antisemitic material last Thursday.
Both Irving and the Nets on Wednesday said they would each make donations of $500,000 after the seven-time All-Star posted a link to controversial film 'Hebrews to Negroes: Wake Up Black America'.
That money will go towards causes and organisations "that work to eradicate hate and intolerance in our communities."
Silver said in a statement on Thursday: "While we appreciate the fact that he [Irving] agreed to work with the Brooklyn Nets and the Anti-Defamation League to combat antisemitism and other forms of discrimination, I am disappointed that he has not offered an unqualified apology and more specifically denounced the vile and harmful content contained in the film he chose to publicise."
NBA boss Silver added that he will be meeting with Irving in person next week to discuss the situation.
Irving said last weekend he would not "stand down" and pointed to the "historical complexities" of African heritage in America, but he subsequently deleted the social media post that sparked the uproar.
In Wednesday’s joint-statement from Irving, the Nets and the Anti-Defamation League, Irving said: "I oppose all forms of hatred and oppression and stand strong with communities that are marginalised and impacted every day. I am aware of the negative impact of my post towards the Jewish community and I take responsibility.
"I do not believe everything said in the documentary was true or reflects my morals and principles. I am a human being learning from all walks of life and I intend to do so with an open mind and a willingness to listen. So from my family and I, we meant no harm to any one group, race or religion of people, and wish to only be a beacon of truth and light."