Thirty-eight men and two women are under investigation after 13 victims came forward alleging abuse between 1997 and 2015, the agency said.
The alleged victims were aged between 11 and 26 at the time the offences are said to have taken place.
Suspects aged between 29 and 53 from Sheffield, Rotherham, Leeds, Dewsbury and Maidstone in Kent have been arrested or interviewed by appointment since March.
All have been released under investigation or bailed while enquiries continue.
The probe is part of Operation Stovewood, the National Crime Agency’s (NCA) investigation into Rotherham grooming gangs. The operation has previously led to 14 men being jailed.
Chief investigating officer Carl Vessey-Baitson said: “Arresting such a large number of individuals as part of one Stovewood sub-operation shows our desire to listen to victims and bring offenders to justice is not wavering.
“Stovewood is a challenging and complex investigation, with victims and survivors reliving abuse that took place many years ago.
“To date we have engaged with over 410 victims and survivors and have arrested or interviewed by appointment 94 suspects, meaning this is the largest law enforcement investigation into non-familial CSAE [child sex abuse and exploitation] ever undertaken in the UK.
“Conducting such an investigation can only be achieved with the support and coordination of our partners, and South Yorkshire Police and Rotherham Metropolitan Borough Council continue to provide invaluable assistance”.
The NCA previously said it had identified 1,523 potential victims and 151 grooming suspects, but investigators believe there could be another 275 other offenders who it has not yet been able to name.
The agency launched Operation Stovewood, at the invitation of South Yorkshire Police, after Professor Alexis Jay’s 2014 report into the rape, grooming and trafficking of hundreds of children in Rotherham.
The Jay report described how more than 1,400 children had been affected – a figure established by the NCA to be an underestimate.
Some 296 female survivors of exploitation had actively engaged with officers by the end of last year.
The NCA has full control of investigating allegations between 1997 and 2013, with 250 staff working on the case and an annual budget that will soon reach £15m a year.
It is estimated the operation will cost more than £90m by 2024 – the date to which current planning extends.
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