"Honestly, I do not want to speculate or comment. I can only talk about what I am 100 percent sure of... and when I have details and facts," Agwai told journalists at a public event in Abuja shown on television.
Last weekend, presidential spokeswoman Remi Oyo said that intelligence and military security agencies were investigating what she described as a "serious breach of security".
"It's true that the intelligence community -- national and military security agencies -- are investigating what looks like a serious breach of security on the part of some military officers and apparent civilian collaborators," she said.
She confirmed that a "considerable number" of military officers had either been detained, interrogated or released over the incident, but declined to give further details.
Although officials have so far played down fears that Africa's most populous country was at risk of its sixth military takeover since 1966, local press reports Wednesday continued to run reports on the security breach.
Nigeria, which won its independence from Britain in 1960, suffered the first of many military power grabs six years later and has since endured a total of 28 years under various military rulers, including a brutal 30-month civil war.
Agawai denied media reports that last Wednesday's transfer of Hamza al-Mustapha, the former security chief under the late military dictator Sani Abacha, from a civilian prison to a military intelligence facility was "an abduction".
The Nigerian prisons service said last Thursday in a statement that al-Mustapha had been released to agents of the Directorate of Military Intelligence for questioning on "matters of national security".
Al-Mustapha, who was seen as Abacha's right-hand man during his 1993-1998 rule, was on remand in Kirikiri maximum prison on charges of having ordered the attempted murder in 1996 of a newspaper publisher who had fallen out with the regime.