
Officials said a sixth person was killed and two were injured during an exchange of gunfire at a makeshift roadblock in the north of the territory on Saturday.
Three indigenous Kanak residents, aged 17 to 36, and two police officers were previously confirmed to have been killed.
More than 200 people have so far been arrested and around 1,000 extra officers have been sent to join the 1,700 personnel already in the territory.
Pictures from the territory showed rows of burned-out cars, makeshift roadblocks, and long queues of people outside supermarkets.
Authorities have declared a state of emergency involving a night-time curfew as well as a ban on public gatherings, alcohol sales, and the carrying of weapons.
Speaking to French news channel BFMTV, external, Ms Lagarde said the last two nights had been calmer, but that the situation during the daytimes was not improving.
“Quite the contrary, despite all the calls for calm,” she said.
She said it was “impossible” to quantify the damage already done but that the burned buildings included municipal buildings, libraries, and schools.
“Can we say that we are in a besieged city? Yes, I think we can say that,” she said. “It is desolation.”
She added that security forces “need to be given a little time” to secure the situation.
Residents reported hearing gunfire, helicopters and “massive explosions” believed to be gas canisters exploding inside a burning buildding.
Helene, 42, who has been guarding makeshift barricades in shifts with neighbours told AFP: “At night we hear shooting and things going off.”
Tourists stranded in the territory have described having to ration supplies while they wait for a way to leave.
Joanne Elias, from Australia, who is at a resort in Noumea with her husband and four children, said she had been told to fill a bathtub in case the water ran out.
“The kids are definitely hungry because we don’t really have much option of what we can feed them,” she said.
“We don’t know how long we’re going to be here for.”
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