Mohammed Bolari, who was at the rally, in the northeastern city of Gombe, said the explosion happened at 3:10 pm (1410 GMT) some three minutes after Jonathan's departure.
A local reporter, who asked not to be identified, said: "The president had just passed the parking lot and we were trailing behind his convoy when the explosion happened... Just 100 metres from the bus we were driving in."
Jonathan had been speaking to supporters of his ruling Peoples Democratic Party (PDP) as part of his bid for re-election at polls in two weeks' time.
There was no claim of responsibility for Sunday's attacks but the city has been hit by suspected Boko Haram militants in the past and suspicion was likely to fall on the Islamist group.
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Bolari said of the latest blast: "It is difficult to say how many people were affected because of the confused struggle by the huge crowd leaving the venue to escape for fear of another blast."
The local reporter said that the explosion led to unrest in the city, with crowds of angry youths attacking anyone seen with any PDP signs.
"We had a difficult time passing through these crowds. At one point a crowd threw stones at our vehicle. Some reporters sustained cuts from smashed window screens.