The Campaign Against Anti-Semitism says Twitter's policies on hateful material are "failing".
Out of about 1,000 anti-Semitic tweets it reported, Twitter found only about 40% breached its policies, it said.
According to Twitter, anti-Semitism breaks its rules and is not permitted on the platform.
This is not the first time Twitter has been accused of being too slow to remove anti-Semitic posts.
Last year it faced accusations it had not acted quickly enough to delete anti-Semitic tweets posted by UK grime artist Wiley. The star later apologised for tweets that "were looked at as anti-Semitic.".
At the time, the prime minister's official spokesman said Boris Johnson believed Twitter "needed to do better", adding: "Social media companies need to go further and faster to remove content like this."
After that incident, and following protests by the group, Twitter invited the Campaign Against Antisemitism (CAA) to become a "Twitter partner", allowing it to report problematic tweets to its staff directly through the company's "partner portal".
But the group claims that hateful material is still widespread and not being removed.
In one December day alone, the group said it discovered anti-Semitic tweets praising Hitler, calling the holocaust a hoax, and accusing Jewish people of controlling the government. According to Twitter, most of these accounts had been suspended for breaking Twitter's rules.
It said of 239 tweets it submitted to Twitter in December 2020, only 43 were found to violate Twitter rules. The group said there was little difference between those tweets that were permitted and those that were prohibited.
The group also alleged a promised series of monthly meetings with Twitter to discuss anti-Semitism were cancelled after just one discussion and that the firm had "cut off contact".
The CAA's Stephen Silverman said: "If Twitter brought us on as a partner as some sort of fig leaf for its inaction, we are now laying bare the true picture of the company.
"It is clear that the company is neither capable nor interested in tackling anti-Semitism, and it must now fall to an independent regulator to assume that role instead."