The agency said that deaths rose by more than 5,500, bringing the global total to 917,417.
The biggest increases in infections were reported in India, the US and Brazil.
Worldwide there have been more than 28 million confirmed cases, half of which have been in the Americas.
The previous one-day record for new cases was on 6 September when the WHO reported 306,857 new infections.
According to the WHO, India reported 94,372 new cases on Sunday, followed by the US with 45,523 and Brazil with 43,718.
More than 1,000 new deaths were recorded in the US and India while Brazil said 874 people had died from Covid-19 related illness in the past 24 hours.
India has the second largest number of confirmed cases in the world, behind the US. Last week it reported nearly two million Covid-19 cases in August, the highest monthly tally in the world since the pandemic began.