Jatuporn Prompan, who heads the pro-government Red Shirt movement, made the comment during a rally in Bangkok that was held three days after prime minister Yingluck Shinawatra was ousted in a ruling by the Constitutional Court.
Punctuating the warning of violence, unknown assailants fired two grenades late on Saturday at the prime minister's office compound, where pro-government protesters were camped. Two people were slightly wounded, said an official.
Emboldened by Ms Yingluck's removal, anti-government protesters ramped up their efforts to bring down what remains of her administration by laying siege to television stations, surrounding state offices and demanding lawmakers help them install a non-elected prime minister.
Ms Yingluck's cabinet has named deputy premier Niwattumrong Boonsongpaisan as acting prime minister, but the leader of the anti-government protest movement, Suthep Thaugsuban, said Mr Niwattumrong "doesn't hold the authority to be the head of the government".
Mr Suthep said the Senate should "quickly consult the presidents of the Supreme Court, the Constitutional Court, the Supreme Administrative Court and the Election Commission to work to appoint the new prime minister immediately".
Thailand's political crisis began in 2006 when Ms Yingluck's brother, former prime minister Thaksin Shinawatra, was toppled by a military coup.