Mr Matthews also said BAA only plans to use runways for both take-off and landings in quick succession - so-called "mixed-mode" - at peak times of the day and only once the airport has improved its record on flight delays.
Transport Secretary Geoff Hoon has said any expansion approvals will come with "stringent" environmental criteria.
Both BAA and the airport's biggest tenant, British Airways, have described the third runway as "vital" to the UK economy.
The Conservatives and Liberal Democrats oppose the idea of a new runway, as do environmental groups, while some backbench Labour MPs are calling for a rethink.
Shadow transport secretary Theresa Villiers said: "We have seen this all before.
"What BAA needs to realise is that people do not want a third runway, we do not need a third runway, and under a Conservative government there will not be a third runway."
Liberal Democrat transport spokesman Norman Baker said: "This is a worthless promise, as BAA has to stick to EU emissions limits anyway."
John Sauven, of Greenpeace, said: "If BAA builds a third runway at Heathrow there is simply no way the airport will avoid breaking pollution limits. That's a fact."
Wandsworth Council leader Edward Lister, speaking on behalf of the 2M Group of councils opposed to Heathrow's expansion, said: "No-one will believe claims by either BAA or the government that flights will be cut in the future in the light of environmental concerns."
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