"Thailand would like to thank the UN secretary-general for closely following in the ongoing political conflict," Sek Wannamethi, director-general of the ministry's Department of Information, said Friday.
"Thailand, as a member of the UN, has to respond to the UN's proposal and listen to its advice."
Mr Sek said the UN secretary-general had been invited to visit Thailand soon to meet different sides, listen to their opinions and observe the overall situation. The UN has experience in jointly finding solutions, he added.
The request to the UN has raised eyebrows among critics of the caretaker government and the Pheu Thai Party.
Commentators have pointed out that the party's de facto leader, Thaksin Shinawatra, famously declared that "the UN is not my father" in response to UN criticism of his human rights record as prime minister more than a decade ago.
On Thursday, UN spokesman Martin Nesirky confirmed at a daily media briefing that Mr Ban did have a telephone conversation with caretaker Foreign Affairs Minister Surapong Tovichakchaikul to discuss Thailand's political situation.
"Well, I think the Thai [media] have reported a telephone conversation with the foreign minister, and I confirm that there was such a telephone conversation," Mr Nesirky said.
He said the secretary-general was closely monitoring the situation in Thailand and was concerned about the recent violence.
Mr Surapong, an adviser to the Centre for Maintaining Peace and Order (CMPO), told reporters on Wednesday that he had spoken to Mr Ban and was considering inviting him to give advice on conflict resolution to prevent other countries losing confidence in Thailand.
"If we could bring the UN in to initiate talks, a solution to the conflict might be reached," he said. "I talked on the phone to Ban Ki-moon to discuss this matter."