London's £496m Olympic stadium is expected to be full to capacity only a few times during the 2012 Games.
The stadium's roof is designed to cover two thirds of spectators
Minister Lord Davies told peers the 80,000-seater stadium would be full for the opening and closing ceremonies and "two or three" of the biggest events.
Lord Davies had been asked why only 68% of seats were to be covered by a roof.
He also said "seating and structures" from the stadium, which is to be cut in size after the games, could be used for the 2014 Glasgow Commonwealth Games.
The exchanges came during the question time at the start of House of Lords business on Monday.
Lord Davies was asked why the roof could not cover all the seats in the stadium. He replied that, to his knowledge, there was no international athletics stadium with total roof cover.
Tory peer Lord Glentoran then said the minister could at least take "great comfort" from the fact the exposed seats would only be filled a few times.
Lord Davies agreed, replying: "There will of course be full attendance of the opening and closing ceremonies, and perhaps two or three of the really major events here at the Games.
"But I think it will be recognised that even for the Olympic Games attendance drops from full capacity for most Olympic events although they are extraordinarily well supported when one normally expects only about 25,000 people at athletic events and in the Olympic Games it is more than double that."
Work will begin on the stadium in April 2008, and once it is over it will be reduced to a 25,000-seat venue so it can continue as a "working athletics stadium" rather than turning into a "white elephant, almost a sepulchre to sport".
Asked what would happen to the spare seats and the roof, Lord Davies said the idea was that the "seating and structures" of the stadium would be moved elsewhere - pointing out that Glasgow would be hosting the Commonwealth Games two years later.
In response to a question from Tory peer Lord Mawhinney he said there were no plans for a major athletics event at the stadium ahead of the games.
But he said the hope was it could be used in 2011 for national and possibly international schools athletics meets, in order to test out the "strengths and any potential weaknesses" of the stadium's arrangements and give the staff some experience.
Crossbencher Countess Mar suggested raincoat manufacturers deserved to share in the profits of the Games and that international spectators should "share in our rather perverse delight of sitting on soggy wet benches with rain pouring down the backs of our necks".