Conte seized power in a coup in 1984 coup and has refused to relinquish his position despite increasing protests and violence.
Last year, a series of strikes led to mass protests before Conte imposed martial law and ordered tanks on to the streets killing dozens of protesters.
Although the unions did not force Conte to step down, last year's strike brought important concessions, including the naming of a new prime minister from a list approved by the unions.
Kouyate was granted wide-ranging powers including the final decision on governmental appointments and firings.
The secretary-general of the National Confederation of Guinean Workers (CNTG), Rabiatou Serah Diallo, told a news conference: "We are going to stage an unlimited general strike to force the government to respect these agreements.
"One would say that there are some people who want Guinean blood to be spilled again."
Police used tear gas to fight back hundreds of protesters who rioted in the poor suburbs of the capital following the news that Justin Morel Junior, the communications minister, had been dismissed by the president according to Bakary Drame, the commander of a security force unit in Conakry.
Soldiers manned busy crossroads in the centre of town, but the protesters dispersed as night fell.
"We are not going to accept this decree," said one demonstrator. "The president does not have the right to dismiss a minister without consulting the prime minister."
Many commentators had expected Kouyate to tender his resignation after the dismissal of his ally, but the street protests and strike call appeared to strengthen his hand.
After an emergency cabinet meeting on Friday, Kouyate's government came out in favour of trying to negotiate between the unions and Conte.
Saidou Diallo, a spokesman for the cabinet, said in a televised statement: "The cabinet recommended that the prime minister meet with civil society, the institutions of the republic and the head of state so the best decisions are taken to assuage the troubles caused by the communication minister's removal."