The explosion in packed Meskel Square came after weeks of sweeping reforms that had shocked many Ethiopians after years of anti-government tensions, states of emergency, thousands of arrests and long internet shutdowns.
The sources cited Ahmed Shede, Government Communication Minister, as saying that investigation is going on the police authorities who are in custody and the result will be announced to the public.
The man with the grenade was wearing a police uniform, witness Abraham Tilahun told the AP.
President Kenyatta urged Prime Minister Abiy to continue the task of uniting the Ethiopian people, ensuring the stability of the country and sustained growth of its economy. "I saw some five people injured following the blast".
"Whoever is trying to darken our joy and love, dilute our unity, you will not succeed", Abiy said in comments televised by the Ethiopian Broadcasting Corp. following the explosion, which happened shortly after he addressed a crowd of supporters.
Eritrea, which has always been at loggerheads with Ethiopia over a border row that Abiy has sought to resolve, condemned the incident. He also said he was ready to implement a peace deal with neighbouring Eritrea, which was signed in 2000.
Overall, thousands of prisoners, including several senior opposition leaders accused of charges such as incitement to topple the government, have been pardoned since January - even before Abiy's election by the EPRDF. Ethiopia had refused to accept the deal's handing to Eritrea of key locations, including the town of Badme, which it still holds. But war veterans in Badme oppose the peace initiative, with some residents saying they will not leave the town.
Eritrean Ambassador to Japan Estifanos Afeworki said on Twitter that his country strongly condemns the attack. Abiy hails from the Oromo ethnic group, making up roughly a third of the population.
Video footage later showed Abiy being rushed from the scene by security guards.