Around 10,000 people have fled north to Sudan from South Sudan where government troops and rebels have battled for the past month, the U.N.'s refugee agency said on Sunday. "10,000, this is something we are confident with, that these are confirmed people who have crossed the border, who have been fleeing the conflict," Nicolas Brass, external relations officer with the United Nations High Commissioner for Refugees (UNHCR), told Agence France Presse. The figure makes Sudan, from which South Sudan separated in 2011, the second-largest recipient of refugees from the battles between forces loyal to President Salva Kiir and those of his ex vice-president Riek Machar. About 32,000 refugees have fled to Uganda and a total of about 10,000 others have gone to Ethiopia and Kenya, the United Nations says.