The Ethiopian government has been asked by rights group Amnesty International to disclose the identity of 35 people arrested more than 10 days ago.
They were accused of plotting to overthrow the government.
The group says more people have been detained since, including an 80-year-old man in need of medical attention.
The government says those arrested were all members of the opposition group founded by the exiled mayor of Addis Abba, Berhanu Nega.
The BBC’s Elizabeth Blunt in the capital, Addis Ababa, says he was one of the most charismatic opposition figures at the time of the last elections in Ethiopia in 2005.
But he was arrested after the polls along with other prominent opposition figures and tried for treason, sentenced to life imprisonment, then pardoned and released.
Along with several of his colleagues he travelled abroad after his release, she says.
But while most of the others have returned to Ethiopia and are now organising themselves as a legitimate opposition party to fight next year’s elections, Dr Berhanu chose to stay in the US, saying that the situation in Ethiopia was such that the government could not be changed by constitutional means.