The phrase 'total war' was used by Chad's President Idriss Deby following a meeting of countries neighbouring Nigeria held in Paris in mid-May, designed to define a common strategy to fight the Islamist group.
Jonathan also said he had authorized security forces to use "any means necessary under the law to ensure that this is done. I assure you ... that these thugs will be driven away. It will not happen overnight, but we will spare no effort to achieve this goal."
It was not clear what such an offensive could entail given that the northeast of the country plagued by Boko Haram insurgents has been under a state of emergency and a full scale military operation for a year - and Nigerian forces are stretched to breaking point.
"With the support of Nigerians, our neighbours and the international community, we will reinforce our defence, free our girls and rid Nigeria of terrorists," Jonathan said.