A French court in January ordered the company to provide the data after legal action by France's Union of Jewish Students (UEJF) and four anti-racism groups.
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Twitter said in a statement that it had given information to judicial authorities "enabling the identification of some authors" of anti-Semitic and racist tweets.
It said the move "puts an end to the dispute" with the groups and that the two sides had "agreed to continue to work actively together in order to fight racism and anti-Semitism".
Twitter said it would also cooperate on "measures to improve the accessibility of the procedure for notifications of illicit tweets."
The UEJF launched a civil suit against Twitter and its CEO Dick Costolo in March claiming 38.5 million euros ($50 million) in damages over the global social networking site's failure to respond to the French court order. The group said it would hand over any damages won in court to the Shoah Memorial fund.
The groups had been pressing Twitter to exercise tighter control following a deluge of anti-Semitic messages last year posted under the hashtag #unbonjuif (#agoodjew). Twitter later removed some of the offending tweets.
President Francois Hollande had also called on Twitter to comply with the court order.
UEJF President Jonathan Hayoun said Twitter's move was "a great victory in the fight against racism and anti-Semitism" and "a big step in the fight against the feeling of impunity on the Internet".
"This agreement is reminder that you cannot do anything you want on the Internet. Twitter will no longer be a conduit for racists and anti-Semites where their anonymity will be protected," he said.
UEJF lawyer Stephane Lilti said the agreement should lead to Twitter making it easier for users to signal racist or anti-Semitic tweets for removal.
The dispute was seen as a test case pitting the right to free expression on the Internet against laws banning hate speech.
In October, Twitter suspended the account of a neo-Nazi group in Germany following a request from the government in Berlin.
That was the first time that the US firm had applied a policy known as "country-withheld content", which allows it to block an account at the request of state authorities.
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