India, in its latest update to the World Organisation for Animal Health (OIE), reveals pockets of the disease close to its western and eastern borders.
India reported late last month that nearly 18,000 horses had been affected in the outbreak.
Its latest report shows cases in Matheran and Raigad, in the state of Maharashtra, with 418 cases among the 465 horses potentially exposed to the disease.
In Pune, also in Maharashtra, there have been 304 cases, with 2813 horses potentially susceptible.
In Kolkata (Calcutta), in West Bengal, there have been 20 cases among horses used by the mounted police.
In Delhi, there have been 49 cases, with 1353 horses potentially susceptible to the highly contagious disease.
"The event is continuing," said the report, submitted by Natarajan Gokulram, secretary in the Department of Animal Husbandry, Dairying and Fisheries, Ministry of Agriculture, based in New Delhi.
The outbreaks have seriously disrupted racing in parts of India.
The first outbreak was in the village of Katra, late in June, and the second, centred on the village of Anantnag, began on July 7.