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Two sieges in France have been brought to a bloody end, with three gunmen and four hostages killed, the BBC reported.

Two brothers who killed 12 in an attack on Charlie Hebdo magazine on Wednesday were shot dead as they fled a warehouse north of Paris, firing at police.

Shortly afterwards in eastern Paris, anti-terrorist forces stormed a kosher supermarket where hostages were being held by a gunman with reported links to the brothers.

The gunman and four hostages died.

French police believe the captives were killed before the assault on the Hypercasher supermarket near Porte de Vincennes, Paris prosecutor Francois Molins told reporters late on Friday.

Four hostages were seriously injured and 15 were rescued unhurt. Two police officers were injured.

The operation was launched after the end of the siege in Dammartin-en-Goele, 35km (22 miles) north of Paris.

The two brothers there, Cherif and Said Kouachi, came out of the building firing at police and were killed. Two police officers were injured.

One hostage there had earlier been released and a second employee, who was hiding in the building's cafeteria, was freed by police after the shooting ended.

French President Francois Hollande described the events as "a tragedy for the nation."

In a televised address, he thanked the security forces for their "bravery [and] efficiency", but added that France still faced threats. "We have to be vigilant. I also ask you to be united - it's our best weapon," he said.