NEW YORK — Twitter on Friday agreed to hand over about three months’ worth of tweets to a judge overseeing the criminal trial of an Occupy Wall Street protester, a case that has become a closely watched fight over how much access law enforcement agencies should have to material posted on social networks.

The social networking site had been threatened with steep fines if it did not comply with Judge Matthew Sciarrino Jr.’s order to turn over the records in the case of Malcolm Harris.

But the judge said he would keep the records sealed until after a Sept. 21 hearing challenging his ruling on the messages.

Twitter’s lawyer, Terryl Brown, called the options it faced — waiving its right to appeal or being in held in contempt of court — “unfair” and “unjust,” though ultimately Brown handed over a thick white envelope full of Harris’ information.

“We are disappointed that Twitter is essentially giving up the fight,” Harris’ attorney Martin Stolar said after the court hearing.

The Manhattan district attorney’s office said Harris’ messages could show whether he was aware of the police orders he’s charged with disregarding during a protest at the Brooklyn Bridge.