The strikers, who have paralysed the West African nation, are demanding Conte's resignation saying he is unfit to rule.
In the working-class Enco 5 district on the outskirts of the Conakry, gangs of youths throwing stones fought running battles with police who fired back with rubber bullets.
Witnesses in Kissidougou said several thousand people had taken to the streets before their rally was broken up, and residents in Kankan, another eastern town, reported a big demonstration.
Troops on the streets
Troops from the presidential guard have been deployed on the streets of Conkary since Monday, alongside police and gendarmes, after the city governor banned all public gatherings.
The only significant public statement from the authorities came on Tuesday night, when the parliament speaker went on television and radio to broadcast some economic concessions on Conte's behalf.
Leaders of the National Union of Workers of Guinea and the Syndicated Union of Workers of Guinea said Conte had failed to address their key demand that he send Mamadou Sylla, the former head of the national bosses' organisation, and Fode Soumah, a former government minister, back to jail.
"We're keeping up the strike and demonstrations across the territory," Yamadou Toure, head of the the National Organisation of Free Trade Unions of Guinea, told AFP on Thursday.
"We haven't closed the door to negotiations, but we need a serene climate. The authorities have really not allowed us to explain our problems," he added.
Conte, who is 72 years old, has run Guinea since a bloodless military coup in 1984 but suffers from diabetes and amnesia and was twice hospitalised last year.