Dozens more were seriously injured in the violence in the capital Conakry and several towns across the country.
President Lansana Conte named Eugene Camara as prime minister on Friday, meeting a deadline to avoid strikes.
However, the demonstrators say Mr Camara is too close to the president and are demanding a leadership change.
Capital 'in chaos'
The violence erupted in the town of Kindia about 140km (85 miles) from the capital, Conakry. At least four of the deaths happened there.
As well as the known seven civilian deaths, there are also unconfirmed reports that two soldiers were killed and their bodies burnt by protesters in the town of Kankan.
The BBC's Will Ross in Conakry said the capital was in chaos on Saturday after protesters went on the rampage, ransacking government offices and the homes of government ministers.
Mr Conte had agreed to hand over the running of the government by Sunday in order to avoid the resumption of an 18-day strike which unions ended last month.
But people are angry that Mr Conte has chosen a close ally for the post of prime minister.
""We cannot go against the will of the people. The president has made a choice which suits him but does not suit the people,"" said union negotiator Boubacar Biro Barry, the Reuters news agency reported.
Military response
Mr Camara has been in government for several years and worked as the minister for presidential affairs.
The deteriorating situation in Guinea is also causing concern for some of its neighbours - Liberia, Sierra Leone and Ivory Coast - says BBC Africa editor Martin Plaut.
""The decision will have concerned many in the region,"" he said. ""The last thing west Africans needed was another crisis that could easily spill across this region's porous borders.""
Sierra Leone and Liberia are only now recovering from years of civil war. Ivory Coast is deeply divided and southern Senegal has a long-running separatist movement.
Some 60 people died during the recent strikes, called over falling living standards and alleged mismanagement.
Guinea is mineral rich but has also been described as the most corrupt country in the world, and most people live in abject poverty.
The president seized power in a 1984 coup but has since won three elections. Now in his seventies and suffering ill-health, there is an overwhelming desire for him to step down.
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