Iturrizaga won four consecutive national championships from 2005 to 2008, and has been playing for Venezuela at the Chess Olympiad since 2004. His best performance came at the 37th Chess Olympiad (2006), when he scored 8.5/11 points playing second board. The result earned him an individual bronze medal. He qualified for the Chess World Cup 2007 after a shared first place at the American Continental Championship. He was set to face Peter Svidler in the first round, but forfeited the first game due to getting lost between Russian airports. He lost the second game. In 2008, Iturrizaga won an online qualifier for the C-group in the 2009 Corus Chess Tournament, defeating GM Alexandr Fier 3-1 in the final. He ended up on a shared eight place out of fourteen in the main tournament, scoring 5.5/13. Iturrizaga finished second in the 2008 Ibero-American Championship in Linares, Spain, losing to Julio Granda in the final. Iturrizaga was the last person to arrive at the tournament, had to play one game at night, and nearly arrived late for one of the matches.