His comments came as Air Miles re-launched its website, designed to allow consumers to redeem their points and book flights and holidays online.
It is part of the company's strategy to be seen as a wider travel brand, as opposed to one that offers free flights only.
"I think this presents us as an aspirational brand and puts clear blue water between ourselves and Nectar," said Thomson. "Good luck to Nectar, but it is not an aspirational reward scheme."
A Nectar spokesman responded: "The difference between Nectar and Air Miles is that we are much broader. There is a crossover, so it's a little misleading to suggest that Nectar doesn't compete with Air Miles.
"Being broader means that Nectar is more of a brand for the people," the spokesman added.
Thomson also claimed the new-look website was not a response to Nectar because it was "planned well before Nectar launched". He said the slump in air travel has not affected Air Miles.
"When seats on airlines are not full, we can offer them to members for less. In the first three months of this year, air travel was down 20 per cent but our business was up 15 per cent," he said.
Air Miles' site now allows members to book hotels, car hire and travel insurance as well as flights. It was developed by web designers Syzygy and went live this month. It was supported by a national roadshow through 18 major towns and cities.