Police distributed photos and other details of the two suspects on Sunday, and said they were Nigerian citizens.
"An arrest has been made by the police in connection with the incident," the police statement said.
"Police detectives are currently hunting for another two Nigerian citizens suspected to be the masterminds of the evil plot. Their names (are) Chima Orlu and Ben Jessy".
The statement signed by Emmanuel Ojukwu, the national police spokesman, contradicted information he had provided earlier that three people were arrested.
"These operators of an evil enterprise had targeted to commit mass murder of innocent children, young and old men and women, and members of the international community who had gathered to partake in our nation's glorious moment."
"The ugly incident resulted in the death of 10 persons, while 36 others, including 11 policemen, were seriously injured," the police statement said, despite Abuja police having given the figure as 12.
Ojukwu did not immediately respond to requests for clarification and an Abuja police spokesman could not be reached.
Al Jazeera's Yvonne Ndege, reporting from Abuja, said that authorities could not seem to agree on the details of the case.
"The two statements from the Nigerian government, apart from contradicting each other, fly in the face of evidence out there about the attack, that shows that the Movement for the Emancipation of the Niger Delta were behind the attack."
The Movement for the Emancipation of the Niger Delta (Mend) claims to be fighting for a fairer distribution of oil revenue.
Our correspondent said that the fact that Henry Okah, Mend's leader who lives in South Africa, had his house raided on Thursday by Interpol, who said they were acting on information from the Nigerian government who said he was planning to bomb Abuja.
"They were also reports that British intelligence had information that men were planning something so they advised Gordan Brown to cancel a scheduled appearance at the Independence celebrations. Add to that the fact that Mend called foreign journalists at least three times before the bombs went off."
Authorities have argued that tightened security had kept attacks from occurring at the main venue of the independence celebrations. The bombs went off about a 10-minute walk away.
Earlier on Sunday, Goodluck Jonathan, Nigeria's president, implicated a "small terrorist group" outside Nigeria in the car bombings and cast doubt on a claim of responsibility believed to be from Nigerian militant group Mend.
"It is a small terrorist group that resides outside Nigeria that was paid by some people within to perpetrate the dastardly act," he said, according to a statement released by his press office.
Source: Al Jazeera and agencies