"As of yesterday (Tuesday), the number of deaths stood at 813," he told reporters in Abuja after a cabinet meeting. "As of now, we are noticing a decline.
"This is week 16. This is also expected because we are moving away from the active season. We are confident that in the next couple of weeks everything will be over."
The outbreak of meningitis C is concentrated in northern Nigeria, where a mass vaccination programme has begun to limit its spread.
Five northern states accounted for the majority of cases.
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Nigeria lies on the so-called "meningitis belt" of sub- Saharan Africa that stretches from Senegal in the west to Ethiopia in the east, where outbreaks are a regular occurrence.
Early prevention of the disease, which is spread through coughs, sneezes and close contact, was hindered by a lack of available vaccine for the type of meningitis C strain responsible.