Kursova tied for first place with Natalia Pogonina, placing second on countback, in the 2003 European U18 Girls Championship, and was the bronze medalist in the 1998 European U12 Girls Championship. She competed in the Women"s World Chess Championship 2006 as FIDE president nominee. Kursova defeated Zhao Xue in the first round, but she was eliminated in the second one by Ekaterina Kovalevskaya.
She plays for Armenia since 2011.
She played for the Armenian team in the Women"s Chess Olympiads of 2012 and 2014, Women"s World Team Chess Championships of 2011 and 2015, Women"s European Team Chess Championships of 2011 and 2013. Kursova is married to Armenian grandmaster Arman Pashikyan.