Around a hundred troops, military trucks and two helicopters were deployed in a failed hostage rescue bid in Sokoto in which an Italian and Briton were killed, witnesses said on Friday.
As Italy seethed over how it had been kept in the dark about Thursday's deadly raid in the northwestern city of Sokoto, witnesses said the captors and the security forces waged a gun battle lasting seven hours.
At least two hostage-takers were killed in the operation along with British national Chris McManus, 28, and Italy's Franco Lamolinara, they added.
Nigerian President Goodluck Jonathan blamed the deaths of the hostages on members of the Islamist group Boko Haram, which has waged a violent campaign mainly in the northeast of the country. He said the killers had been arrested.
But local residents of the calm but hot and dusty city of Sokoto, the base of Nigeria's supreme Muslim leader, the Sultan of Sokoto, disagree the Islamist group was behind the kidnapping.
"We don't believe it," a 40-year-old businessman living in the neighbourhood told AFP. "They are kidnappers. We don't have Boko Haram in Sokoto."
Sokoto sits on the border with Niger, on the southern edge of the Sahara desert.
British Prime Minister David Cameron meanwhile took responsibility for authorising the operation to rescue the two expatriate engineers who were kidnapped in May.
His Italian counterpart Mario Monti convened a security committee meeting over Britain's failure to consult Rome before approving the rescue bid.
Italy's President Giorgio Napolitano was quoted as saying that the failure to inform Rome about the bid was 'inexplicable'.
While officials gave few details about the operation or those involved, newspapers in London said that it had included members of the British elite forces Special Boat Service (SBS) who had been in Nigeria for a fortnight.
Residents said at least 100 soldiers were involved in the operation.
They came in two trucks and a tank and blocked the entrance to the house.
"At around 11 am I saw soldiers coming... uncountable, about 100. They started firing," said the businessman, asking not to be named.
Another resident earlier said "around 100 troops surrounded the area."
The kidnappers apparently tried to flee the troops by scaling a wall into a next-door house which was partially built.
Soldiers asked residents for old tyres which they lit and tossed into the building in a bid to smoke the kidnappers out, then engaged them in an intense gun battle, the witnesses told AFP.
"After the shootout had been going on for about seven hours, the soldiers gained access into the house," said a witness whose house is directly opposite.
"Initially they brought out two dead bodies I believe to be white men, followed by two bodies of dark-skinned people I believe to be among the gunmen," said the witness.
The witness reported seeing three men taken out of the house in handcuffs. They also said a private security guard at the uncompleted house was killed in crossfire.
Bullet holes poked the walls of the two houses which were unguarded on Friday. Residents walked in and out at will.
British and Nigerian authorities had been concerned from the start that the kidnappers were Islamist extremists as they had ignored a large amount of cash that the men had stored in the apartment where they were abducted, according to British media.
Cameron said the bid to rescue the men had been authorised after "a window of opportunity arose to secure their release".
He said the two hostages were held by "terrorists" who had made "very clear threats to take their lives", and they had been in "imminent and growing danger".
Britain's Foreign Secretary William Hague said that there had been "limited time" and too many "constraints" to consult Italy ahead of the operation.
British media said that Nigerian intelligence officials had tracked the group to Sokoto. GCHQ, Britain's intelligence listening centre, identified and monitored the telephone calls of the gang.
Around a dozen members of the SBS had been helicoptered in to rescue the hostages on Thursday, British reports said.
Residents said two helicopters had hovered over the middle class Mabera neighbourhood mid-morning on Thursday before the shootout broke out.
AFP received a video showing McManus and Lamolinara in August. In the footage, both men said their kidnappers were from Al-Qaeda.
Al-Qaeda in the Islamic Maghreb, has in recent years claimed kidnappings of foreign workers in countries including Niger, which borders Nigeria to the north, but never in Nigeria.
The two were kidnapped by heavily armed men from their apartment in neighbouring Kebbi state in May 2011. They were working for a construction firm Stabilini Visinoni which was helping build a central bank office in the city.
Boko Haram has been blamed for increasingly deadly and sophisticated attacks in Nigeria, Africa's most populous nation and largest oil producer.