The government on Tuesday shrugged off efforts by the Student Union of Thailand (SUT) to drum up public support for the ouster of Prime Minister Prayut Chan-o-cha.
Asked about the SUT's "Wing Lai Lung" (Run to Oust the Uncle) event, Gen Prayut said he would leave it to the public to decide which side to take.
"In the end, society will decide if this political move makes sense under the current peaceful political situation," said Gen Prayut, who has been nicknamed "Lung", or Uncle.
Asked about a counter-move to hold a similar event in his support, the premier quipped: "Run to catch up with me if you can."
A group of Gen Prayut's supporters on Tuesday announced on Facebook a "Wing Tam Lung" (Run to Follow the Uncle) event to back Gen Prayut.
Deputy Prime Minister Prawit Wongsuwon shrugged off the developments, saying merely that both groups were entitled to run.
"These running events are fine as long as their organisers do not violate the law on public gatherings," he said. Asked whether he would take part in either event, Gen Prawit joked: "How could I manage to join a run? These days I can't even walk steadily."
The Wing Lai Lung run also carries the English name of "Run Against the Dictator" and will be held on Jan 12 in central Bangkok.
The event made headlines when Thai Glico Co and Glico Frozen (Thailand) Co cleared up confusion over the run's logos on Monday by announcing they had nothing to do with the political movement and were always politically neutral. The companies urged organisers to withdraw their "Glico Running Man" logo, a doctored version of Glico's trademark, since it had resulted in widespread misunderstanding that Glico was sponsoring the event.
The Glico Running Man is an internationally recognised trademark that has lit up the Japan-based firm's Osaka headquarters for more than 80 years.
SUT chief strategist Tanawat Wongchai said on Facebook that Glico's trademark was not used by the campaign for commercial purposes or with any intent to damage Glico's reputation.