Suthep stuck to his demands and urged the military to back him, telling it he was not calling for a coup, but that "if you make a decision soon, the people will see you as a hero of the people, and we can solve the problem."
Thanasak said the sides must reach a "solution that fixes everything for the long term, and does not return things to the same cycle."
The military's interventions in recent decades have been messy. In 1992, the army shot dead dozens of pro-democracy demonstrators protesting a military-backed government in the streets of Bangkok, the capital, and in 2010 repeated the bloodshed in quashing another uprising.
The army's 2006 coup against Prime Minister Thaksin Shinawatra Yingluck's brother was a bloodless one, but was followed by the installation of an inept interim government. The coup also polarized the country, which has seen Thaksin's supporters and opponents contending for power ever since, sometimes violently.
Suthep and his group want new laws to banish corruption in politics to be implemented ahead of any election. The protesters say Thai politics are hopelessly corrupt under the alleged continuing influence of Thaksin, who has lived in self-imposed exile since 2008 to avoid jail time on a corruption charge.
Yingluck has dissolved parliament to call elections for Feb. 2.
More significant than what Suthep said Saturday was the role the armed forces played in hosting the event.
The military, apparently seeking to cast itself in a new light, has repeatedly declared itself neutral in the current political battle, though it's no secret that it dislikes Thaksin.
Despite being wanted by police on an insurrection charge, Suthep sat on a stage during Saturday's forum, which was attended by the leaders of the various military branches. The commander of the national police force, whose leadership and ranks are generally pro-government, was invited but did not attend.
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Associated Press writer Jinda Wedel contributed to this report.