Abhijit in his career as an Indian chess player has represented India in four occasions at chess Olympiads (1998-2004) and bagged seven medals in the Asian Team Chess Championships (team bronze medal in 1999, two team and individual silver medals in 2003, team gold and bronze individual medals in 2005, team silver and individual bronze medals in 2008).
In the year 2000, Abhijit played in the single elimination tournaments for World Chess Championship (once in Delhi and then in Tehran) where he faced defeat in the knockout stage to Gilberto Milos.
Years later in the year 2007, Kunte took the bronze medal at Cebu City's Asian Chess Championship and played in the chess world cup in 2007(Khanty-Mansiysk) where lost a knockout match to Vadim Zviagintsev).
He shared and won many championships at Kolkata (Calcutta) 1998, Blackpool 2003, Kolkata 2004, New Delhi 2005, Guelph 2005, Kitchener 2006 and Mumbai (Bombay) 2008.
Awards for Abhijit Kunte
He was awarded the Grandmaster title in 2000.