Abdulsalami spoke to journalists on Wednesday at his home in Minna, the Niger State capital.
His admonition is coming a few days after some persons were killed in a market in Oyo State during a clash.
Newsmen reported how several people reportedly died in a clash in a conflict between Hausa and Yoruba groups in the state.
The crisis was triggered by an alleged stabbing of a Yoruba cobbler by a Hausa cart pusher in Shasha market, Ibadan.
Governors of Bauchi and Benue states last week also engaged in tense verbal exchange over arms bearing by Fulani herdsmen.
While Governor Bala Mohammed of Bauchi State justified arms bearing by the herdsmen, his Benue counterpart, Samuel Ortom, condemned his statement.
The Nigerian Governors Forum had, however, said the Shasha crisis was not ethnic in nature.
Newsmen quoted Abdulsalami, a retired general, as saying that the recent spread of violence across the country, if not carefully handled, might lead Nigeria to a point of no return.
He called on all Nigerians, especially the governors of the 36 states of the federation, “to take full responsibility in managing the divergent voices and frustrations within their states which he said could fuel disunity, anarchy and disintegration”.
He urged the governors to be united and respect individual views. The former military leader, who is also the Chairman of the National Peace Committee, cautioned that disunity, coupled with insecurity could push the country to the point of no return.
“As if the continued insurgency in the country, the kidnap and armed robbery are not cup full, the recent happenings in some parts of the country, of ethnic attacks, is unfortunate and is adding to the problems,” Abdulsalami said.
“In the last two weeks or so, tension has been growing in the country and embers of disunity, anarchy and disintegration are spreading fast and if care is not taken, this might lead us to a point of no return.
“We at the National Peace Committee, wish to add our voice to the voices of millions of Nigerians calling for calm in these difficult times because these times demand that we all join hands to resolve our challenges so as to keep our country united. We do not have the luxury of trading blames.
“Thousands of our people are homeless and have refugees across the length and breadth of their own country.
“We know the difficulties that our farmers have faced in the last few years and that the harvests will be a serious challenge this year.
‘’Therefore, let us all rally in these hard times, make the required sacrifices and remain vigilant, standing by one another.’’
“It is true that we are all in a state of fear and collective anxiety. However, the last thing we need is for the enemy to sense a lack of unity on our part or a break in our ranks.”