"We believe we are going to have a huge influx (of fans), 1.3 million during the tournament", said Khater, speaking as Qatar unveiled its first fully refurbished World Cup venue, the Khalifa International Stadium.
He is at least the fourth World Cup employee to have died of cardiac arrest in the past year and a half, the newswire states.
Rights group have alleged labour abuses at Qatar World Cup sites.
His death was not due to his working conditions, organisers said. "Our sympathies are with his family at this time", said the Supreme Committee statement.
He added: "I think everybody when they think of a World Cup, they expect the majority of the fans are going to be coming from western Europe and South America".
Amnesty International's 2016 report The Ugly Side of the Beautiful Game: Exploitation of Migrant Workers on a Qatar 2022 Site, highlighted how migrant workers were exploited at the Khalifa Stadium. In addition, a law making it easier for the migrant workers to change jobs and leave the country came into effect in December a year ago.
"Qatar's World Cup organizers have placed special requirements on contractors that are supposed to stop this happening, but the reality is that workers on their sites still live under Qatar's repressive sponsorship system, which gives employers powerful tools to abuse them".
SC secretary general H.E. Hassan Al Thawadi said: "The completion of our first stadium more than five years before the Qatar World Cup begins is an important milestone that reflects our determination to deliver a tournament the entire Arab world is proud to be a part of".
Qatar's government has denied claims there are higher instances of heart attacks among construction workers and does not publish independently verified statistics on worker-related injuries and fatalities.
The 40,000 Khalifa International Stadium has been open since 1976 but has been extensively renovated for the major competition in the middle eastern country.
Autopsies and post-mortems on people who die sudden and unexpected deaths are forbidden by Qatari law unless a crime is suspected.