Demonstrators erected burning barricades and tried to attack government offices in towns across Guinea, clashing with security forces as they did so.
Camara was appointed on Friday in a move aimed at avoiding a repeat of last month's general strike that left 59 people dead.
But Conte's opponents say Camara is too close to the ruling clan to be a trustworthy head of government.
Renewed violence
Looters smashed their way into shops in parts of the capital, Conakry, while rocks and the charred remains of barricades littered main streets in the suburbs.
Residents in the Bonfi suburb said the security forces had killed one civilian and injured another when they opened fire on youths who started stoning a passing convoy they believed to be transporting the president.
"Two people were hit. One of them died, he was hit in the head," one witness said.
At least two people were killed in Kankan, 450 km (280 miles) east of Conakry, when a military police officer opened fire on demonstrators before himself being beaten and burned to death, residents said.
Two people were killed in Faranah, 300 km east of Conakry, while a local government official in Kindia, 100 km northeast of the capital, said between three and five civilians had been shot dead when they tried to storm a prison.
Strike call
Boubacar Biro Barry, one of the unions' main negotiators, said: "The president has made a choice which suits him but does not suit the people."
"We contest this choice and the strike order launched as of Monday is maintained."
Another union leader also said the nomination of Camara, formerly Conte's minister in charge of presidential affairs, was not enough to call off a nationwide stoppage planned from Monday.
"We asked for a clean prime minister.
Instead of that we get an old man from the old guard who is too close to the current power structure," Louis Mbemba Soumah, secretary-general of the SNECG teachers' union, said.
"For us the strike order is maintained."
Strike leaders, who say Conte is no longer fit to rule after 23 years in power, had given the president until Monday to name a new premier, as he agreed to do in a deal struck two weeks ago to end an 18-day nationwide stoppage.