The three are part of a group of nine bloggers and journalists accused by police of "serious crimes", with the other six having appeared in court a day earlier. Thursday's hearing was held in closed session.
None have yet been charged, with police requesting more time to investigate their case.
"The detainees told the presiding judge that they were beaten by the police investigators under their feet and slapped and punched on their faces," defence lawyer Amha Mekonen told AFP.
But she said the police had denied the claim, saying "no one had touched" the detainees.
On April 25 and 26, six members of the blogging collective Zone Nine and three journalists were arrested by police, with the government saying they were being investigated for "serious crimes", without elaborating.
The arrests prompted an outcry from rights groups, with the Committee to Protect Journalists (CPJ) calling them "one of the worst crackdowns against free expression" in the country, while Amnesty International said it was part of a "long trend of arrests and harassment of human rights defenders."
Ethiopia has one of the most closed press environments in the world, the CPJ says, with at least 49 journalists forced into exile - a figure only beaten by Iran and Somalia.
Ethiopia has also been accused of cracking down on independent media and doling out heavy sentences for journalists under controversial anti-terror legislation.
The six who appeared in court Wednesday will next appear on May 17. The three in court Thursday will next appear on May 18.
US Secretary of State John Kerry urged Ethiopia to allow greater freedoms for civil society and journalists, during a visit last week, expressing concern for the group.
UN human rights chief Navi Pillay has condemned the arrests, warning the country is increasingly muzzling freedom of expression under the guise of fighting terrorism.