Boko Haram is trying to expand its activities beyond Nigeria's mainly Muslim north, to include the commercial capital Lagos, as well as other parts of the country, officials say.
Nigeria's intelligence agency says 12 members of the Islamist militant group have been arrested in Lagos since July.
It is not possible to independently verify details of the statement.
Boko Haram has waged a six-year insurgency in Nigeria, mainly in the north-east of the country.
Authorities arrested other self-confessed Boko Haram members in the south-eastern city of Enugu as well as other parts of central and northern Nigeria, the Department of State Services (DSS) said in a statement.
The DSS attributes the attempted expansion of Boko Haram into southern areas to the increased pressure the group is under in its north-eastern heartland.
However, the BBC's Will Ross in Lagos says the group is still causing havoc in the north-east, with reports that more than 50 people were killed in an attack in Borno State on Friday, about 100km (62 miles) north of the state capital Maiduguri.
Will Ross, BBC News, Lagos
For many in Lagos it will be alarming to hear that a dozen Boko Haram members have been arrested here in recent weeks. I have often been told by Lagosians that the jihadist group would never dare attack this city, which seems more naive than reassuring, especially as there was an attempt to bomb a fuel depot last year.
The announcement from the secret police, known as the DSS, came just a day after another statement told us a teenager had been picked up inside Abuja airport where he was gathering intelligence for Boko Haram - another disturbing bit of news.
The DSS says the arrests have helped avert "devastating attacks" and that "notable commanders and frontline members" have been rounded up.
We have no way of independently verifying the information in the statements but it is worth noting that all the security departments are under pressure to demonstrate that they are having an impact against Boko Haram, especially as President Muhammadu Buhari has made tackling the jihadist insurgency a priority and is still making senior appointments.
A new DSS director general was appointed in early July and the latest statement says the arrests began the very next week.
Boko Haram at a glance:
- Founded in 2002, initially focused on opposing Western-style education - Boko Haram means "Western education is forbidden" in the Hausa language
- Launched military operations in 2009
- Thousands killed, mostly in north-eastern Nigeria, abducted hundreds, including at least 200 schoolgirls
- Joined Islamic State, now calls itself "West African province"
- Seized large area in north-east, where it declared caliphate
- Regional force has retaken most territory this year