Rescue workers are combing the site for an estimated nine people, including two children, who are still unaccounted for, a spokesman for the French capital's firefighter service said.
It was unclear how many people were in the building when the explosion rocked the street in the north-eastern suburb of Rosny-sous-Bois shortly before 8 am (0600 GMT), as some may still be away for the summer vacation.
A gas leak was likely to have been the cause of the blast, Interior Minister Bernard Cazeneuve and police said.
Gabriel Plus, a commander of the fire brigade, noted that there were gas works on site, although he would not draw a direct link with the disaster.
Among the fatalities is a child. An elderly woman also succumbed to her injuries.
"She died while we were extracting her from the rubble," said Plus.
The force of the blast shook buildings as far as 100 metres from the site.
"Our house moved, we were trembling from fear," said Pauline. The explosion was so loud that "our ears were ringing," she added.
Others ran out into the street to help victims.
Ghislaine Poletto, 55, who lives about 50 metres away, said she "jumped into her trousers" and hurried to the site where together with neighbours "we managed to pull two children out".
One of the children was "protected by a mattress and a board above his head which saved his life," she said.
A nearby school has been requisitioned by local authorities to host families hit by the blast.
Deputy mayor Serge Deneulin said the building dates to the 1970s and was "in perfect shape".
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DATELINE:BOBIGNY, France, Aug 31, 2014 (AFP) -
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