Prime Minister Jean-Marc Ayrault described the island's accelerating descent into lawlessness as "intolerable" and said the government would issue new instructions to the authorities there on tackling crime.
"The government is determined to act against the plague of organized crime in Corsica," Ayrault said.
President François Hollande added: "The violence in Corsica is not new but it has changed in nature and intensity. It is today essentially linked to (criminal) networks, clans, feuding that has led to the number of deaths increasing incessantly in a way that is completely unacceptable."
Antoine Sollacaro, a well-known advocate with links to Corsica's intertwined worlds of armed nationalism and mafia-style criminal clans, was killed in a professional 'hit' on his way to work on Tuesday.
It was the 15th murder of its kind this year on a Mediterranean island that is equally well known for its idyllic combination of spectacular mountains, pristine beaches and balmy climate. Since the start of last year there have been 37 murders and 117 attempted killings.
On an island with 310,000 inhabitants, that means the murder rate is roughly four times that of Marseille, traditionally seen as France's capital of crime.
Gang violence in Marseille in late August prompted calls for the army to be called in but the slayings on Corsica had, until now, provoked little discussion in the corridors of power in Paris.
That changed in the wake of Tuesday's killing of Sollacaro, a lawyer who was famous for defending Yvan Colonna, the Corsican nationalist who spent four years as France's most-wanted man after escaping arrest for the 1998 assassination of France's top official on the island, the prefect Claude Erignac.
Colonna, a shepherd, was finally arrested in a mountain refuge in 2003, convicted of Erignac's murder and sentenced to life in prison.
Stung by allegations that the French state has accepted its inability to impose the rule of law on Corsica, Interior Minister Manuel Valls promised he would visit the island next month.
"We can't just stand back and admit our impotence in the face of this mafia, this gangrene in Corsican society," Valls said.
The investigation into Sollacaro's murder is being handled by an anti-mafia team of detectives based in Marseille.
Overall responsibility for combatting serious crime on Corsica is shared between them, police on the island and an anti-terrorism unit in Paris, which has primary responsibility for monitoring nationalists involved in bomb attacks on symbols of French rule over the island.
Paul Giacobbi, the chair of the island's executive council, said rivalries and overlaps between the three forces had allowed crime to flourish.
"There is practically no political violence on Corsica any more," he said. "We have to stop recounting fairy tales, it's all about the mafia."
The Corsican National Liberation Front (FLNC), which is waging a campaign for the island to be granted independence, tends to concentrate its attacks on targets it sees as symbols of French rule.
Last month it claimed responsibility for seven explosions at supermarkets and other retail outlets on the island. It has also claimed 20 attacks on second homes across the island in May and the bombing of a property complex at Balistra in July. None of the attacks resulted in injuries.