Kassai refereed in UEFA Euro 2008 as the fourth official in several matches. During 2008, he also officiated in the 2008 Olympic Games, including in the final.[2]
On 5 July, it was announced that he would be in charge for the Germany vs Spain semifinal. It was his fourth match in the World Cup. This is the highest prestige match a Hungarian referee has been in charge of since Sándor Puhl's 1994 FIFA World Cup Final.
His first appearance in the 2010 FIFA World Cup was a group stage match between Brazil and North Korea on 15 June 2010, which Brazil won 2–1. He refereed two matches in the group stage. The United States vs Ghana match finished after extra time, becoming the first match in the World Cup to happen so. It was the first time that either Ghana or the United States played in a World Cup match ending in extra time.
At the UEFA Euro 2012, Kassai officiated matches Spain vs Italy and England vs Ukraine. This was the first international tournament where two additional assistant referees were introduced on the goal-lines.[4] During the England and Ukraine game a Ukrainian strike was cleared by English defender John Terry, but TV re-plays showed that the ball had crossed the line.[5] This led to a debate on the effectiveness of the inclusion of the two additional officials and the need for goal-line technology.[5]FIFA president Sepp Blatter said, "goal-line technology was a necessity" following the England vs Ukraine match.[6]
On 9 January 2020 he was appointed the head of refereeing department of the Russian Football Union.[8] He resigned from the position on 13 September 2021.[9]
On 26 January 2022 Kassai was appointed the head of refereeing department of the Bulgarian Football Union.[10] He will be in this position until the end of June 2023.[11]
