"Since November 6, there have been no reports of the elk behaving aggressively so the cull has been suspended,” local police said in a statement published online.
However, the creature could still be legally hunted and killed if it moves away from the area previously covered by the cull order. This year's elk hunting season in Sweden ends on February 28, 2018.
On Monday this week, police in Eda in the Värmland area of Sweden permited a "preventative hunt" of the animal for a limited period, carried out by a specific hunter, after it attacked a member of the public.
This sparked a public outcry, led by local mayor Hans Nilsson, who pledged to act as a human shield for the elk. Nilsson also launched an online campaign to protest against the cull, which garnered some 14,800 signatures in 48 hours.
The animal has been affectionately named Ferdinand by local people, after the bull in the 1936 book by Munro Leaf. A clip of the Disney film version of the book is shown every Christmas on Swedish Television.
Footage of Ferdinand wallowing in a stream - taken by Nilsson in August - went viral, prompting worldwide interest in the animal.
Local police chief superintendent Christer Lööf told Radio Sweden that there are an estimated 50 to 100 white elk in Sweden, 90 per cent of which are believed to be in Värmland. The total elk population in Sweden is several hundred thousand.