The group's leader Abubakar Shekau said in a new video posted on Twitter late on Tuesday evening that his fighters would disrupt polling in Africa's most populous nation scheduled for March 28.
"This election will not be held even if we are dead. Even if we are not alive, Allah will never allow you to do it," he said in the Hausa language widely spoken in northern Nigeria.
Shekau also claimed responsibility for a large-scale attack on the northeastern city of Gombe last Saturday where leaflets were dropped warning people not to vote.
Attahiru Jega, president of the Independent National Electoral Commission (INEC), has been criticised for agreeing to the postponement on security grounds.
National security advisor Sambo Dasuki recommended pushing back the date from February 14 to give troops in a regional offensive against Boko Haram more time to secure and stabilise the northeast.
The deployment would leave soldiers unavailable to provide security on polling day, he said.
But Dasuki's six-week deadline to effectively crush the militants has been seen as unrealistic, even if it allows INEC more time to distribute more ID cards to the 68.8 million registered voters.
Two suicide attacks -- one at a checkpoint near Biu in Borno state and another hours later in a restaurant in Potiskum in Yobe -- killed at least 38.
Many of the victims at the first were children.
The bombings were the latest in an increase in violence since the start of the year and linked to the elections, which Boko Haram views as un-Islamic.
