Sargissian played for Armenia in the Chess Olympiads of 2000, 2002, 2004, 2006, 2008, 2010 and 2012. He took team bronze medal in 2002 and 2004 and team gold medal in 2006, 2008 and 2012. In the 2008 Chess Olympiad he won the gold medal for his individual performance on board three (+7 −0 =4 with an Elo performance rating of 2869). He was a member of the gold medal-winning Armenian team at the World Team Chess Championship in Ningbo 2011. He also played for Armenia in the European Team Chess Championships of 2007, 2009, 2011, 2013 and 2015, winning team silver medal in 2007 and 2015, and individual gold in 2009. Sargissian played for "MIKA Yerevan" in the European Chess Club Cup in 2008, 2009, 2010, 2011 and played for "CA Linex Magic Mérida" (Spain) in the 23rd European Chess Club Cup in Kemer 2007, winning team gold medal.