Interior Minister Manuel Valls on Monday told the TV station Canal+ that anti-terrorist investigators have "serious leads" on the identity of the person who stabbed French soldier Cedric Cordier in the neck while he was patrolling an underground shopping center and transport hub near Paris with two colleagues, Radio France Internationale reported.
Police described the attacker as just over six feet tall and having a beard.
District Prosecutor Robert Gelli told French television that security cameras showed the alleged assailant wore a black sweater and black pants before he fled into a crowd at a subway and train entrance plaza.
Cordier, 23, fell to the floor instantly after being stabbed. He was reported out of danger Monday after being rushed to a military hospital. Doctors said the assailant narrowly missed a vital carotid artery in Cordier's neck.
French President Francois Hollande refused to say the attack had anything to do with the gory killing of a British soldier on a London street Wednesday. The British government called that attack, allegedly by a pair of homegrown Muslim extremists, an act of terrorism.
"He left without saying a word," Gelli said.
The prosecutor's counter-terrorism department is leading the investigation, Le Monde reported Monday.
Hollande said in a televised statement from Ethiopia, where he was on a state visit, security authorities should "look at all the possibilities" as they investigated the assault.