Election body chairman Attahiru Jega announced the postponement for presidential and parliamentary polls from February 14 to March 28 late yesterday, citing guidance from the national security advisor (NSA).
Gubernatorial and state assembly elections will be held on April 11.
The NSA, Sambo Dasuki, had written to Jega last week explaining that security could not be guaranteed on February 14 because all available military resources had been committed to an intensified operation against Islamist rebels in the northeast.
"They say they need six weeks to defeat Boko Haram. Boko Haram has been growing for six years... If in six weeks Boko Haram has not been defeated, they could call for another delay and ultimately destroy Nigerian democracy," he added.
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The vote was expected to see the ruling Peoples Democratic Party (PDP) face its first serious electoral challenge since the end of military rule in 1999.
Many observers believed that the opposition All Progressives Congress (APC), led by ex-military ruler Muhammadu Buhari, had seized the momentum in the campaign against Jonathan.
The APC called the postponement "highly provocative" and "a major setback for democracy" but appealed for calm.
The US said it was "deeply disappointed" by the delay, with US Secretary of State John Kerry warning the Nigerian government against using "security concerns as a pretext for impeding the democratic process."
The PDP said it welcomed the postponement because "it was in the best interest of democracy."