"Deforestation rates are still very high, but this year we will have the smallest deforestation rate of the past 21 years," he said.
A peak of 27,329sq km was cleared in the 2003/2004 period, Minc said.
Policy and economy
The drop may allow Brazil to claim some success at delivering on a pledge to reduce deforestation during a major world climate summit in Copenhagen this December.
The government has been under pressure to slow the encroach of loggers and ranchers for decades, while attempting to develop the resource-rich region.
Deforestation has in the past increased when demand for soya beans, beef and timber have gone up, and officials point out that when police attempt to confiscate lorries loaded with illegal wood, the situations can turn violent very quickly.
Minc attributed 90 per cent of the deforestation reduction to improved policing. And while experts give authorities some credit for the trend, they say lower commodity prices resulting from a global economic crisis also was a factor.
The states with the biggest reduction were Rondonia and Mato Grosso, both in the southwestern region of the Amazon. The worst performing state was Mato Grosso, whose governor is often called the "king of deforestation" by conservationists.