Abbas has participated in the two most prestigious tournaments in international field hockey seven times: FIH Hockey World Cups in 1998, 2002 2006 and 2010 and three Olympics in 2000, 2004 and 2012, scoring in all of them while being the top scorer at the 2002 World Cup and 2004 Olympics with 10 and 11 goals respectively. He has also appeared in the former Hockey Champions Trophy organized by FIH eight times from 1998 to 2011 being the top scorer for Pakistan in the competition with 41 goals. He has scored 54 goals against India, most goals against a single opponent. He has scored 74 international goals at the Malaysia National Hockey Stadium in Kuala Lumpur, his most at a single venue.