Prime Minister Dominique de Villepin and Interior Minister Nicolas Sarkozy vowed everything would be done to catch the perpetrators who targeted the bus in the southern city of Marseille on Saturday night.
A 26-year-old Senegalese university student who was trapped on the bus after two hooded teenagers doused it with petrol and set it alight was on Monday in hospital in critical condition, with burns to 60 percent of her body.
The attack was the worst incident in a surge of urban violence over the weekend that coincided with the first anniversary of the riots that shook France last year.
Sarkozy said the gang responsible would be brought to justice.
"Believe me, we will find them," he said after an emergency meeting with Villepin and transport chiefs.
"This is a promise I made to the family" of the woman, Mama Galledou, Sarkozy said. "And this promise will be kept."
Villepin said he looked to toughening laws against those involved in such attacks, including against minors.
He also urged witnesses to come forward, anonymously if they chose, so that the arsonists could be "brought before the courts."
Police in Marseille said they had few leads so far but were working on the theory the young attackers lived in the neighbourhood.
"We're going all out. Thirty to 35 investigators are at work, and all the crime squad is on this," Marseille state prosecutor Jacques Beaume said.
President Jacques Chirac and other politicians have expressed their "horror" at the attack.
The head of the hospital burns clinic treating the woman, Jean-Claude Manelli, said that while she had survived the crucial first 36 hours, "we can't make any prognostic for the days to come."
He said her face, legs, arms, hands and throat were burnt, exposing her to breathing, neurological and infectious problems.
She was on artificial respiration and in an artificial coma. Her family was with her but declined to comment.
Gellidou was on the bus with some 10 other passengers when it was forcibly boarded by the two teenagers wearing hoods while the third stood outside. They doused the inside of the vehicle with flammable liquid and set it on fire before running away.
Although the driver and other passengers escaped in time, the woman was unable to do so.
A witness, who gave his first name as Alain, told AFP that he vomited after seeing the result.
"Her skin, it looked like gloves had been taken off her... She's a black woman and her skin had been burned white... and she had nylon trousers -- you know what happens when nylon melts?" he said, his voice becoming hoarse.
Bus drivers in Marseille and Nice resumed work on Monday after stoppages to protest the attack.
Two hundred extra riot police were deployed to Marseille to provide extra security.
Elsewhere in France, police reinforcements were also standing by after the weekend wave of violence.
According to police, nine buses were torched across the country last week, seven of them in the Paris area, by hooded or masked youths, some of whom were armed, though no other serious casualties were reported.
Scores of parked cars have also been incinerated, and overnight on Sunday, youths threw a stone from a bridge on a tram in the eastern city of Grenoble, smashing the window and injuring the driver.
Some 30 cars were torched in nearby Lyon the same night.
Scores of arrests have been made in scattered skirmishes with police, and several officers were slightly hurt.
In the Paris suburb of Clichy-sous-Bois on Saturday, a 16-year-old boy was shot in the eye by a flashball gun, a non-lethal weapon increasingly used by French police. His father said the injury was unprovoked and left the boy blind in that eye.
The violence recalled the three weeks of riots that raged in mostly poor French suburbs a year ago -- the worst civil strife the country has seen in four decades.
Then, gangs of youths, most of them from families of African and Arab origin living in marginalised neighbourhoods, torched more than 10,000 cars and firebombed 300 buildings in around 275 towns.

Copyright AFP (Agence France-Presse), 2006