Last year, authorities indicated a slightly lower figure of 5,843 square kilometres for a 28 per cent rise.
That reversed several years of decline despite being the second lowest annual increase since records began in 1988.
The official Institute of Special Investigations (INPE) unveiled the amended figure yesterday showing Para state in the north and the central western state of Mato Grosso as the worst affected areas.
The worst year on record was 2004, with 27,000 square kilometres of forest destroyed.
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Deforestation in the Amazon River basin region, the world's largest rainforest, fell to a low of 4,571 square kilometres (1,765 square miles) in 2011/2012.
The rise across 2012/13 coincided with the passing of a reform of Brazil's forestry code reducing the amount of forestry cover landowners are required to maintain, infuriating environmentalists.
The INPE is set to publish the August 2013-July 2014 data by year's end.
First indications based on monthly satellite observations through to July of this year are that deforestation increased by 9.8 per cent for a second straight year.