In his first video message, posted on YouTube, 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.
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 leaders of the Igbo ethnic group tried to secede.
In the 15-minute video, Mr Shekau, wearing a red and white turban, a bulletproof vest and sitting in front of two Kalashnikov rifles, said he was responding to recent statements from President Goodluck Jonathan and the leader of the country's main Christian organisation, the Christian Association of Nigeria (CAN).
He warned President Jonathan that Nigeria's security forces would not be able to defeat the group.
"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.
CAN head, Pastor Ayo Oritsejafor, had said on Saturday that his members would protect themselves against the attacks, which he said suggested "systematic ethnic and religious cleansing."
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.
What the Christians did to them. What did the Christians do to them? Who can give a record of the uncountable number of Christians that have being killed since the inception of the north and the sick religion called islam in Nigeria? I don't know what the Christians will do if they were to avenge the death of their uncountable number of brothers killed. They'll probably have to kill every muslim in the world to make up for it! For how long shall the wicked prevail against the righteous? O God! arise and slay your enemies! Let them know that Your are the God of the Christians!
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