Prosecutors said they would not demand the death penalty and called for jail sentences from five years to life for the group.
Media rights groups have accused Addis Ababa of using national security concerns as an excuse to clamp down on opposition figures and journalists, a charge dismissed by the government, Reuters reports.
Writer Eskinder Nega was arrested last year and accused of trying to incite violence with a series of online articles, alongside other charges.
Along with the 23 other named individuals, he was also accused of belonging to Ginbot 7, a group branded a "terrorist" organisation by the Ethiopian government.
The 24 were charged last year, most of them in absentia, with six counts including conspiracy to dismantle the constitutional order, recruitment and training for terror acts and aiding Ethiopia's arch-foe Eritrea and a rebel group to disrupt security.
Only Nega and seven other defendants were in court on Wednesday when judge Endeshaw Adane dismissed charges of espionage and participation in terror acts. The rest were abroad and convicted in absentia.
Adane said the defendants' main aim was to spark an "Arab Spring"-style revolt in the country.
"Under the guise of freedom of speech and gathering, the suspects attempted to incite violence and overthrow the constitutional order," he said before delivering the verdict.
The trial resumes on July 13, when sentences are expected.
Two journalists were each jailed for 14 years on similar charges in February, two months after two Swedish newsmen were imprisoned with 11 years for entering the country illegally and aiding a rebel group.
Critics point to an anti-terrorism law passed after several explosions in 2009 that states that anyone caught publishing information that could induce readers into acts of terrorism could be jailed for between 10 to 20 years.
More than 10 journalists have been charged under the law, according to the Committee to Protect Journalists. The group says Ethiopia is close to replacing Eritrea as the African country with the highest number of journalists behind bars.
Addis Ababa insists its arrests of journalists has nothing to do with their reporting or political affiliations.
Amnesty International and other rights groups have said more than 150 opposition politicians and supporters have been detained since last year on terrorism-related charges.
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