Kalitvintsev earned 22 caps (scored 1 goal) for the Ukrainian national football team. He scored only one goal, but very important one against the group favorites, Croatia, at Republican Stadium in Kiev on 11 June 1995 during qualification to the Euro 1996.
Kalitvintsev was a coach of several junior Ukraine national football teams that played in tournaments for U-19 and U-17 players. Kalitvintsev was appointed as assistant of head coach Myron Markevych of Ukraine's national football team early February 2010. After Markevych resignation of late August 2010 Kalitvintsev was appointed Ukraine's caretaker manager on 25 August 2010. On 21 April 2011 Oleh Blokhin was (again) appointed head coach of the Ukrainian national team; Kalitvintsev stayed on as Blokhin's assistant.