The stadium which has a budget of £496 million and which will seat 80,000 people will be the centrepiece for the 2012 Games.
The Independent newspaper reported on Sunday that the budget for the east London stadium could rise to £540m, a figure refuted by an Olympic Delivery Authority (ODC) spokesman.
ODC Chief Executive David Higgins said: "There is endless speculation about Olympic costs. The stadium budget has been published and remains at £496m.
"We are making great progress on site, starting construction three months early, and are confident the overall budget and contingency is realistic."
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Work has also started on the first venue outside of Olympic Park. The Olympic and Paralympic Sailing events in 2012 will be hosted at the Weymouth & Portland National Sailing Academy.
Work is due to be completed by the end of 2008, meaning Weymouth and Portland is on schedule to be the first venue for the Games.
Mr Higgins said: "The start of construction on the first venue for 2012 is an important step forwards and it is significant we have hit this major milestone in Weymouth and Portland, showing that the London 2012 Games will spread sporting and economic benefits spread around the UK."
Yesterday, the ODC announced that construction of the Olympic Village is on track to start this summer, following the clearance of the area that will link the Village and VeloPark during the Games.
Clearance of the site included the demolition of 28 buildings, including the two tallest buildings on the Olympic Park site – the 12-storey University of East London towers.
Following the Games, the Village will provide around 4,000 homes.
The original Olympic Games were first recorded in 776 BC in Olympia, Greece.
The International Olympic Committee was founded in 1894, the first of the IOC's Olympic Games were the 1896 Summer Olympics, held in Athens, Greece.
(DS)
