In his first video message, posted on YouTube, Abubakar Shekau referred to attacks on Muslims in recent years in several parts of northern Nigeria.
Boko Haram militants attacked several churches on Christmas Day, killing dozens of worshippers.
This has led to some reprisals in the mainly Christian south.
Mosques in two states have been attacked.
Nigeria, Africa’s most populous nation with 160 million people, is divided between a largely Muslim north and a south where most people are Christians and some animists.
Thousands of people have fled their homes following the recent attacks, leading some people, including Nigeria’s president and the leader of the country’s main Christian organisation, to make comparisons with the 1967-70 civil war when the south-east tried to secede.
‘Religious cleansing’
In the latest attack, four people have been shot dead by attackers on motorbikes while they filled up their car with petrol in the north-eastern Yobe state, the local police chief has told the BBC.
Police chief Lawal Tanko did not release the identities of those killed, or the attackers.
The AFP news agency quotes local residents as saying those killed were southerners. Shootings from motorbikes are a Boko Haram trademark.
Yobe state is one of those areas where President Goodluck Jonathan has recently declared a state of emergency but the police chief said he had not yet received the details.
In the 15-minute video, Mr Shekau, wearing a red and white turban, a bullet-proof vest and sitting in front of two Kalashnikov rifles, said he was responding to recent statements from Nigeria’s President Jonathan and the leader of the country’s main Christian organisation, the Christian Association of Nigeria.
He warned President Jonathan that Nigeria’s security forces would not be able to defeat the group.
Mr Jonathan, a Christian, declared a state of emergency in some northern states last month – but the attacks have continued.
On Tuesday night, gunmen opened fire on a bar in Yobe, killing eight people, including several police officers.
The president recently said that he suspected some officials, politicians and members of the security forces sympathised with Boko Haram.
Defending the latest spate of violence, Mr Shekau referred to the killing of Muslims in places like Jos, Kaduna, Zangon Kataf, Tafawa Balewa in recent years.
Some of these places have seen bitter communal clashes but correspondents say they are often based on long-standing disputes over resources such as land, or are whipped up by politicians, rather than being based on religious differences.
“We are also at war with Christians because the whole world knows what they did to us,” Mr Shekau said in the video, speaking in Hausa – the most common language in northern Nigeria.
“They killed our fellows and even ate their flesh in Jos,” he said, referring to reports last year of isolated cases of Christian youths burning and eating their rivals in Plateau state, where more than 1,000 people have been killed in a series of clashes over the past two years.
Christian Association of Nigeria head Ayo Oritsejafor said on Saturday that his members would protect themselves against the attacks, which he said suggested “systematic ethnic and religious cleansing”.
On Tuesday, he told the BBC World Service there should be dialogue with Muslim leaders to halt the violence.
Mr Shekau said the group could only hold talks with the government in accordance with the teachings of Islam.
He said the group’s primary targets remained the security forces, who he said had summarily executed their former leader Mohammed Yusuf after he was arrested in 2009.
“Everyone has seen how we were treated, people have seen what has happened between us and armed security agents and their accomplices who give them information about us,” Mr Shekau said.
After a lull, in 2010 the group started to stage drive-by shootings on government targets in its base in the north-eastern city of Maiduguri.
Last year, it carried out suicide bombings on high-profile targets such as the headquarters of the UN and the police in the capital, Abuja.
The group, known locally as Boko Haram meaning “Western education is forbidden”, wants to establish Sharia law in Nigeria.
