The head of state for the first time claimed direct links between the Sunni radicals who have been waging a six-year insurgency in Nigeria and the Islamic State group in Syria and Iraq.
He told the Wall Street Journal in an interview: "Are they (the United States) not fighting ISIS? Why can't they come to Nigeria?
"They are our friends. If Nigeria has a problem, then I expect the US to come and assist us."
"I can tell you that there are no plans as I speak here to send unilaterally, to send or to add US troops into Nigeria. There are no US troops operating in Nigeria," he told reporters.
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Kirby said the United States was in the early phases of helping establish a multi-national task force of African nations to help Nigeria defeat Boko Haram.
Jonathan's comments were published as hundreds of Islamist fighters invaded the northeastern city of Gombe, firing heavy guns and throwing leaflets calling for locals to shun the elections.
Boko Haram has opened up two new fronts in its campaign to create a hardline Islamic state in northeast Nigeria, pushing into neighbouring Niger last week and for the first time yesterday, Chad.
It has also increased the frequency and intensity of its attacks on northern Cameroon. The increasing regional threat has led to the deployment of troops from all three countries, reflecting security fears.
Jonathan and his government have long sought to portray, the insurgency as being fuelled by outside forces and he has previously called Boko Haram "Al-Qaeda in west Africa".
Boko Haram, which loosely translates from the Hausa language widely spoken in northern Nigeria as "Western education is forbidden", started out in 2002 as a largely peaceful Islamist movement.
But it has been transformed in the last six years from a rag-tag group of guerrilla fighters into a conventional army, seizing territory and dozens of towns in three northeast Nigerian states.