The move came a day after Irving announced he will make a $500,000 donation to groups working to eradicate hate and admitted a film slammed as anti-semitic which he boosted on social media had a "negative impact" on the Jewish community.
Irving ignited a firestorm of controversy last week after posting a social media link to "Hebrews to Negroes: Wake Up Black America" -- a 2018 film widely lambasted for containing a range of anti-semitic tropes that was criticized by, among others, Nets owner Joe Tsai.
Silver, however, wants to see more from Irving than he delivered in a statement announcing the donation, including an apology for his actions and denouncing of the anti-semitic content in the film.
"Kyrie Irving made a reckless decision to post a link to a film containing deeply offensive antisemitic material," Silver said in a statement on Thursday.
"While we appreciate the fact that he agreed to work with the Brooklyn Nets and the Anti-Defamation League to combat anti-semitism 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 publicize.
"I will be meeting with Kyrie in person in the next week to discuss this situation."
In a joint statement, the Nets, Irving and the Anti-Defamation League touched on the topics but without the degree of criticism Silver seeks.
"I oppose all forms of hatred and oppression and stand strong with communities that are marginalized and impacted every day," Irving said in the statement with the Nets.
"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."
The statement declared that the controversy "sparked many emotions" and "brought greater awareness to the challenges we face as a society when it comes to combating hate and hate speech" in announcing the contribution by Irving, which will help create educational programs to fight bigotry and anti-semitism."