By 4pm yesterday, 968 of the 3,000 tickets for 1 January remained unsold.
The New Millennium Experience Company (NMEC) said: "The first ticket sold [to the public] for the Dome was at a National Lottery outlet in Stepney, East London, just before 6am. The second was in Bungay, Suffolk."
Lord Falconer of Thoroton, the Cabinet Office minister in charge of the pounds 758 million attraction, said the entry prices were "extremely reasonable". Single tickets cost pounds 20 and family tickets pounds 57.
He said that the prices reflected the quality of the "experience" on offer, responding to Liberal Democrat spokesman Norman Baker.
Mr Baker had said: "If the Millennium Dome is anything, it should be access for all and the price they are setting is effectively cutting people out and discouraging those with lower incomes."
Tickets are on sale for visits from January to March 2000. The rest will go on sale after Christmas.
Millennium Dome organisers have promised visitors will not experience long queues.
Speaking inside the dome, Jennie Page, NMEC's chief executive said: "We will be using the most advanced visitor management techniques to make sure people don't feel they have to stand in line."
Ms Page said many other visitor attractions operated on 70 per cent of full capacity and some "regarded queuing as a good thing".
But the Dome had been designed to operate comfortably at 100 per cent capacity, with 35,000 tickets every day expected to be sold for off-peak periods and 55,000 for peak periods such as school holidays and the first weeks in January.
Sales took place through all four routes open to members of the public wanting to buy a ticket - National Lottery outlets, through the Internet, by calling the Dome ticket line or simply buying at railway and bus stations.
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