Nigeria's domestic security agency known as the Department of State Services (DSS) advised "that necessary precautions are taken by all."
On Sunday, the United States embassy in Nigeria issued an advisory warning its citizens of an "elevated risk of terror attacks in Nigeria, specifically in Abuja," without giving further details.
"Avoid all non-essential travel or movement," the statement said, adding that it was "reducing services until further notice."
Britain, Canada and Australia issued similar warnings over the weekend, recommending citizens in Nigeria and in Abuja in particular avoid public spaces where crowds gather.
The statements also reminded that schools have been targets for Nigerian insurgents in the past.
DSS spokesperson Peter Afunanya said "The service calls for calm as it works with other law enforcement agencies and stakeholders to maintain peace and order in and beyond Abuja," he said.
In a bid to "de-escalate threats gathered from various intelligence... U.S advisory inclusive," Nigeria's police said it was launching a counter-terrorism exercise in Abuja on Tuesday and Wednesday.
The operation was designed to improve coordination between different units "in response to terrorist incidents and other violent crimes," Adejobi said.
Nigerian police said the public should not "panic at the sounds of explosives and gunshots during the exercise."
In addition to the terrorism threat, the Nigerian capital is also surrounded by states with high levels of banditry -- gangs of heavily armed criminals who kidnap and kill.
Analysts have warned that insecurity could worsen with the start of political campaigning to replace Buhari next year.
