No group has said it carried out the attacks yet but suspicion has fallen on Boko Haram Islamists.
Two separate attacks at a bus station in Nyanya killed 90 people previous year.
A local hospital source told Xinhua that there might be a rise in the death toll, as a few of the injured are now in critical conditions.
The explosions happened in Nyanya and Kuje, both satellite towns of Abuja, agency spokesman Ezekiel Manzo said in a statement.
Senior officials at NEMA on Saturday morning said that the suicide bomber who targeted the Kuje police station died while climbing the fence of the station when the bomb that was strapped to his body went off. At least five villagers were said to have been shot dead by suspected Boko Haram militants in the neighboring state of Adamawa.
“While it is not in doubt that our security agencies are winning the war on terror, these kind of attacks show that there is much work to do about intelligence gathering and sharing”.
There was no immediate claim of responsibility for the blasts.
Nigeria’s President, Muhammadu Buhari, who came to power vowing to eradicated Boko Haram, condemned the attack.
He has given his top commanders until early November to end the fighting, which has claimed at least 17,000 lives and made more than 2.5 million homeless since 2009, creating a major humanitarian crisis.
He noted that the attacks in Maiduguri, Yola and Abuja were apparently timed to coincide with Independence Day celebrations when Nigerians would be commemorating and rejoicing October Day.
A regional force involving 8,700 troops from Nigeria, Chad, Cameroon, Niger and Benin is due to deploy to fight the extremists.