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."
But Pentagon spokesman Rear Adm. John Kirby said there are no plans to send US troops to Nigeria.
"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.
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.
The attack, which began at about 9 am (0800 GMT), saw residents flee and the authorities impose a 24-hour lock-down in the city, which Boko Haram has repeatedly targeted.
Boko Haram has opened up two new fronts in its campaign to create a hardline Islamic state in northeast Nigeria, pushing into neighboring Niger last week and for the first time on Friday, 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-Qaida in west Africa."
Critics have interpreted his attempt to blame foreigners for the violence that has left more than 13,000 dead and displaced more than one million since 2009 as a diversion from national failings.
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.
The group has generally not been thought to have any direct operational links with overseas jihadis, although some fighters may have received training from al-Qaida-linked militants in north Africa.
Boko Haram leader Abubakar Shekau has previously mentioned IS group leader Abu Bakr al-Baghdadi in videos but has not pledged allegiance to the outfit.
The Nigerian group's tactics of extreme violence and mass casualty hit-and-run raids, bombings and suicide attacks also predated those carried out by the IS group.
But Jonathan told the US newspaper that Nigeria had intelligence reports that Boko Haram was receiving "training and funds" from IS militants.
Any direct US military intervention would constitute a marked shift in Nigeria's attitude towards the conflict. It has repeatedly insisted that it can take on the militants alone.
The United States has provided surveillance and intelligence specialists, as well as aerial drones, to help in the high-profile hunt for 219 schoolgirls kidnapped by Boko Haram last April.
But bilateral ties have since been fraught over Washington's refusal to provide military hardware because of concerns about human rights abuses in the Nigerian army.
The latest attack in Gombe, south of Boko Haram's centre of operations, coincided with the original date for presidential elections, at which Jonathan is seeking a second four-year term.
The vote was postponed last Saturday after the electoral commission was advised that regional forces needed more time to tackle the insurgents and would not be able to provide security on polling day.
But the six-week deadline to effectively secure and stabilize the northeast and allow hundreds of thousands of people displaced by the violence to vote has been seen as unrealistic.
Jonathan on Friday maintained that postponing the elections until March 28 would give the security agencies time to "clean up" the three states worst hit by the insurgency for voting to take place.