Strike leaders want the president, a reclusive and amnesiac diabetic in his 70s, to step aside in favour of a consensus government.
A police source said elite army units, including members of the presidential guard wearing red berets, fired into the air to disperse protesters trying to march towards the city centre via a major highway bridge.
"We've managed to disperse them," the source said.
Riot police armed with tear gas launchers and automatic rifles sealed off the city centre.
One witness spoke of seeing four bloodied bodies in one neighbourhood.
The strike turned violent last week.
Strike supporters, some shouting "We want change" took to the streets of several quarters of the city on Monday.
"The marchers have four bloody bodies with them and they say they're heading for the town centre. There are thousands," one resident of the Dixinn neighbourhood, said.
In recent days, Conte has been staying at the central Samory Toure military base instead of his usual residence.
The stoppage has also disrupted the strategic mining industry in Guinea, the world's biggest exporter of bauxite from which aluminium is extracted.
Calls for restraint
The latest unrest flared as religious leaders, union chiefs and government representatives struggled to negotiate a solution to the general strike.
The stoppage has paralysed public transport and shut government offices, schools, shops and markets.
Strike leaders say Conte, who has ruled Guinea since seizing power in a 1984 coup, has become increasingly erratic.
They cite repeated scares about his health, sudden and chaotic cabinet reshuffles and his recent personal intervention to free from jail two former allies accused of graft.
Conte appealed on Sunday for the people and the army to unite behind him and he has offered some concessions and sacked his closest government ally in a bid to appease the strikers.
But union leaders say this is not enough.
"If there are demonstrations in the street it is because this has become a popular uprising. We're not in control of it," said Ousmane Souare, a union negotiator.