Unfit to rule
Union leaders say the reclusive Conte, a diabetic in his 70s, is unfit to rule and are demanding he name a prime minister to run the impoverished West African country.
The two-week-old strike has halted shipments of bauxite from the world's top exporter of the ore, and triggered food shortages in Conakry, the capital, as markets and banks remain closed.
Abdoulaye Sow, deputy head of the powerful USTG union group, said: "The people of Guinea do not want any more promises. They want something concrete.
"It is an agreement in principle. Now it is necessary to put it into practice."
Louis Bemba Soumah, the vice secretary-general of the USTG, said: "The strike is not suspended. And we will not suspend it until we have all that we have asked for. We need guarantees because there is a problem of trust."
There is no obvious favourite to fill the post of consensus prime minister and, diplomats say, any appointee may struggle to end the political crisis as long as Conte's family continues to influence government affairs.
Union leaders want a new broad-based government of national unity to take over with a prime minister to fill a post left empty since April when Conte sacked Cellou Dalein Diallo.
Of the possible new prime minister, Soumah said: "We have proposed that it be a clean, new appointee, who will not be partisan, who will set up a government of technocrats to allow Guinea to finally move."
Conte's clan-based rule has been founded on the support of the army since he seized power in the former French colony in a 1984 coup.
Union leaders had said they could no longer negotiate after soldiers and police opened fire on unarmed protesters on Monday, the bloodiest day of the strike so far.
They returned to the negotiating table after the personal intervention of Conte's wife, Henriette, late on Tuesday.
Hospital officials said at least 33 people were killed in the capital on Monday and more than 150 injured, in addition to at least eight people killed in clashes in the previous days.
Louise Arbour, the UN high commissioner for Human Rights, said in a statement: "The killings have to be investigated expeditiously and impartially, and anyone found responsible for abuses must be brought to justice."
Security remained tight around Conakry on Wednesday but more people ventured out than earlier in the week.
"We're tired. There is no water, no electricity, nothing to eat," said Amadou Toure, 32, a taxi driver.
Some youths gathered on street corners said they were ready to protest if talks failed. But others said Conte's departure seemed less likely than ever after Monday's violent repression.
One restaurant worker said: "It's the government that has won this strike."
Louis Michel, the European Commission aid chief, urged dialogue. The EU resumed aid payments to Guinea just a month ago in return for progress on democratic reforms.
The UN and African Union also criticised the authorities' use of force.