The survey, by Russian, British and Norwegian researchers, showed that bear numbers in the region were at the bottom of previous rough estimates of 3,000-5,000.
Still, "a stock of 3,000 animals is relatively large in biological terms," the Norwegian Environment Ministry said in a statement. The total is about 12 percent of an estimated global population of 25,000 polar bears.
"The count…gives us a good starting point for further protection of this creature. We know that polar bears are exposed to environmental poisons and climate change in the Arctic," Environment Minister Knut Arild Hareide said.
An eight-nation report in November said that the Arctic was warming at twice the rate of the rest of the planet due to global warming, blamed by most scientists on a build-up of heat-trapping gases from burning fossil fuels.
The warming report, by 250 scientists, projected that polar bears could be driven towards extinction by 2100 because polar ice might almost disappear in summers. Some scientists disputed the findings.
Separate studies have shown relatively high levels of a banned "dirty dozen" chemicals, some of which can cause cancers, in the fat of polar bears. The chemicals, including pesticides, are swept north by winds from Europe and North America.