Prime Minister Yingluck Shinawatra has called a snap election that has not satisfied the protesters, whose leader, Suthep Thaugsuban, wants an unelected "people's council" to run the country.
The country's politically powerful army has staged or attempted 18 coups in the past 80 years, including the ousting of Ms Yingluck's brother Thaksin Shinawatra in 2006. But it has said it does not want to get involved this time, though it may mediate.
Deputy army spokesman Werachon Sukondhapatipak said: "The chief of the armed services will not meet Mr Suthep today."
A small group of protesters briefly entered Government House premises yesterday and said they would cut water and power to the complex if police did not withdraw. Police held their positions and there was no confrontation.