The protesters want the current government under Prime Minister Yingluck Shinawatra to step down and be replaced by an unelected "People's Council".
They allege that her government is controlled by her brother, former Prime Minister Thaksin Shinawatra, who is in self-imposed exile after he was overthrown in a military army coup in 2006 and convicted of corruption.
At least four people have died since Saturday, in what has been Thailand's worst political turmoil since the 2010 rallies that ended in violence.
But a senior Thai military official appeared optimistic.
"Everyone agreed that the military forces will not take a leading role in this situation and there will be no coup, as we believe the tension is easing and everything will be back to normal soon," navy chief, Admiral Narong Pipathanasai, told media on Wednesday.