The pro-government "Red Shirt" supporters issued the warning at a rally outside Bangkok - the first staged by the movement near the capital since violent clashes broke out in November. Tens of thousands of people from across the country joined a pro-government rally.
The event has been billed as a last-gasp attempt to save the government led by Yingluck, who is facing mounting legal cases -- including charges of neglect of duty and abuse of power -- that could see her removed from office in coming weeks.
Yingluck's supporters say they are holding the rally to deter her opponents from attempts to oust her.
Jatuporn Promphan, the chairman of the pro-government United Front for Democracy Against Dictatorship (UDD), said judicial institutions were trying "to take over power without elections".
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"What we are most concerned about - that we want to warn all sides against - is a civil war, which we do not want to happen," he said.
"It will happen if there is a coup and democracy is stolen."
As the red-shirts gathered, anti-government protest leader Suthep Thaugsuban rallied supporters 20 kilometres to the east in Lumpini Park for a "final battle".
"Once we become the sovereign, we'll seize the assets of the of the Shinawatra family members. We won't allow them to go abroad. They will need to report to us," he declared.
"We will appoint the prime minister of the people," he said.
The government called a snap election in February, but that was obstructed by protesters. Since then Thailand has been in a state of political paralysis.
The Constitutional Court later nullified the February poll.