Faced with his first major test Gen Abubakar responded with enough force to quell any hopes of a meaningful anti-government demonstration.
Police arrested Gani Fawehinmi, a lawyer and leading dissident who organised the protests. They also arrested Dupe Abiola, one of the wives of the imprisoned businessman Moshood Abiola, the presumed winner of cancelled 1993 elections.
Mr Fawehinmi, arriving at the scene of one of protests, was lifted on to the shoulders of his supporters, but police were so enraged when the crowd began to cheer that Fawehinmi was then arrested along with the men carrying him.
Pro-democracy activists in Africa's most populous nation had promised a day of action to protest against the new military regime, installed last Tuesday following the sudden death of Gen Abubakar's predecessor, General Sani Abacha.
On the anniversary of presidential elections annulled by the army five years ago, they called for the release of political prisoners, focusing on Chief Abiola, who was detained in 1994 on treason charges for declaring himself the victor.
"The only acceptable option for the military is the immediate termination of military rule, installation of a government of national unity to be headed by Chief Abiola and the convocation of a sovereign national conference," said a spokesman for the Civil Liberties Organisation (CLO), one of a plethora of south-western groups opposed to military rule.
The armed forces had seemed anxious. Schools and universities were closed in several parts of the country. General Muhammad Marwa, the military administrator of Lagos state, formerly the seat of government but much marginalised by General Abacha and the main centre of resistance to his rule, had appealed for calm and patience. His police chief, Alhaji Abubakar Tsav, was more direct. "Anyone who engages in any public act capable of breaking the law will be seriously dealt with," he warned.
For the most part Lagos was quiet, with many workers choosing to protest by staying away from work. "I want democracy but I don't want trouble," said one street vendor. "Maybe we should give this new guy a chance." At another small rally in the northern town of Kaduna, protesters carried banners that read, "No fuel, no water, no work, no medicine, military must go now." The demonstration was reported to have passed off peacefully.
Gen Abubakar has still to establish his position four days after finding himself the compromise choice of a divided military. "The next days are crucial" said a western diplomat in the capital, Abuja, "at the moment things could still go either way." Amidst a swirl of speculation in diplomatic circles, Defence Headquarters took the extraordinary step of issuing a statement denying that anything untoward was taking place. "The rumour that some people are under arrest and there is insurrection in Abuja is a lie pedalled by a few disgruntled elements to cause problems for the new administration," said army spokesman, Colonel Godwin Ugbo.
In a brief address to the nation earlier this week, the new head of state committed himself to General Abacha's programme to restore civilian government, but did not say whether this would happen by 1 October, as planned. He said nothing about the fate of more than 100 political prisoners, fuelling speculation about the continuing strength and influence within government of those officers loyal to General Abacha.