Protest leader Suthep Thaugsuban had suggested he and Ms Yingluck should hold a televised debate.
"Ms Yingluck is the legitimate leader of the country and Suthep is a man with warrants for his arrest who heads an illegal movement. The prime minister should not talk to Suthep," said Labour Minister Chalerm Yoobamrung, who oversees a state of emergency imposed in January. "Suthep is only proposing negotiations, even though he dismissed them before, because protest numbers are dwindling."
The protesters have blocked major road junctions in the capital, Bangkok, since mid-January and forced many ministries to close as part of a four-month campaign to push out Ms Yingluck and eradicate the political influence of her brother, ex-premier Thaksin Shinawatra, seen as the real power in Thailand.
A total of 23 people have been killed since November.