"We're confident that we can explain that (Cambodia's claims) are wrong," he said in his weekly television address.
"Cambodia is calling for (intervention by) a third country, the UN and peacekeeping forces. Thailand will call for a return to bilateral talks on demarcation," he said.
Thailand will present evidence including pictures and media reports to support its case and show that Cambodia used an ancient temple at the centre of the dispute as a military base, he added.
Thai Foreign Minister Kasit Piromya is due to attend Monday's Security Council meeting, along with his Cambodian counterpart Hor Namhong.
Thailand and Cambodia have blamed each other for the clashes around the ancient temple of Preah Vihear, which sparked four days of fighting earlier this month.
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