Suazo played for the Honduras national under-20 football team at the 1999 FIFA World Youth Championship. He made his senior debut for Honduras in a May 1999 friendly match against Haiti and has earned a total of 57 caps, scoring 17 goals. He has represented his country in 30 FIFA World Cup qualification matches and at the 2010 FIFA World Cup. He also played at the 2000 Summer Olympics and at the 2003 UNCAF Nations Cup as well as at the 2003 CONCACAF Gold Cup. He also played a few minutes of Honduras' first match at the 2001 Copa América.