Caretaker Foreign Minister Surapong Tovichakchaikul made the appeal while briefing diplomats from 51 countries and said their condemnation of the protesters would not be considered interference in Thailand's domestic politics.
He said the protesters have violated the rule of law and that his request was in line with the United Nations Charter, Bangkok Post reported.
Surapong said the United Nations should take the lead on his call. "I want to see the UN be the first to condemn them."
The Election Commission (EC) could not organise the polls in parts of nine provinces and in entire areas of another nine as there were no candidates registered.
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All nine provinces with no candidates are in the southern region, the political stronghold of the opposition Democrat Party, which boycotted the election.
The EC yesterday offered to broker talks between the caretaker administration and the anti-government People's Democratic Reform Committee (PDRC).
"Both parties need to take a step back, sit down and talk things out," EC chairman Supachai Somcharoen said.
Supachai said the EC believes the political situation would be improved by April.
The EC has said the results of the election will not be announced until polls have been held in all constituencies. This meant that political limbo would continue in Thailand, which has been wracked by years of political unrest.
Yingluck will remain caretaker premier with limited powers over policy until there is a quorum of 95 per cent for the 500 seats in the lower house of parliament to enable the appointment of a new government.
They accuse Yingluck of acting as a proxy for her fugitive brother, ex-premier Thaksin Shinawatra who was ousted in a coup in 2006. He lives in self-imposed exile in Dubai to escape a jail term on a corruption conviction.