Vesković was appointed four times as the head coach for women's national team of Yugoslavia and Serbia. He coached the national team under all four state names: SFR Yugoslavia, FR Yugoslavia, Serbia and Montenegro and Serbia. He coached SFR Yugoslavia national team at the 1991 European Women Basketball Championship where he won silver medal. Vesković coached FR Yugoslavia and Serbia and Montenegro national teams at 1999 EuroBasket Women and 2003 EuroBasket Women.