Al Jazeera's Yvonne Ndege, reporting from Borno state in northern Nigeria, said: "One cannot be a hundred per cent sure of what the police are saying about the capture and death of Mohammed Yusuf for two reason.
"One, the military and police are under sustained political pressure to root out Boko Haram. Two, on Wednesday we were told that Yusuf and at least 300 of his supporters fled Maiduguru as they were being pursued by Nigerian security forces.
"What we have asked the Nigerian police force for is evidence that they have actually captured Mohammed Yusuf but we have not got it."
News of Yusuf's death came after the group's deputy leader was reported to be among dozens of people killed after troops shelled Boko Haram's base in the city of Maiduguri.
Security forces were said to be pressing ahead with the hunt for Boko Haram members on Thursday.
The government warned people to evacuate the area, then shelled and stormed the group's mosque and headquarters on Wednesday night.
A firefight ensued with retreating Boko Haram members armed with homemade hunting rifles, firebombs, bows and arrows, machetes and scimitars.
A reporter for the Associated Press news agency saw soldiers shoot their way into the mosque before opening fire on those inside.
The reporter later counted about 50 bodies inside the building and another 50 in the courtyard outside.
Our correspondent said there has been a "reduction in some of the fighting and that's because the Nigerian security forces have been able to flush out some Boko Haram members".
"It now appears many of the Boko Haram members have fled the scene, but there has been more violence in another state - Kano state - not far from Borno state, where we understand that security forces bulldozed a mosque and a house where the alleged leader was living," she said.
A spokesman for a human rights group said government forces had killed bystanders and other civilians as they battled members of the sect.
But a military spokesman denied the charge and said it was impossible for rights workers to differentiate between civilians and members of the Boko Haram.
Abubakar Umar Gada, a senator from Sokoto state in northern Nigeria, told Al Jazeera that security agents had been deployed heavily and the situation "is totally under control".
He said Boko Haram had "taken advantage of the large number of people who are unemployed" and lacking opportunities to better their lives.
"We largely have a social problem that has been taken advantage of by these miscreants to cause havoc and confusion," Gada said.
Boko Haram, which means "Western education is prohibited" in the local Hausa dialect, has called for the enforcement of sharia even among non-Muslims.
Nigeria's 140 million people are nearly evenly divided between Christians, who dominate the south, and the primarily northern-based Muslims.
Islamic law was implemented in 12 northern states after Nigeria returned to civilian rule in 1999 following years of military rule.
The clashes began on Sunday in nearby Bauchi state, with fighters attacking police stations, before spilling over into Yobe.
Residents said fighters armed with machetes, knives, bows and arrows and home-made explosives attacked police buildings and anyone resembling a police officer or government official in the city.
But most of the casualties appear to have been in Maiduguri, the northeastern city known as the birthplace and stronghold of the group.