The protest escalation came after caretaker Prime Minister Yingluck Shinawatra shrugged off the ultimatum by the People's Democratic Reform Committee (PDRC) led by Mr Suthep that demanded she and her government step down from their caretaker role in 24 hours, or by 10.30pm last night, to pave the way for the appointment of an interim prime minister and the setting up of a "people's council" under Section 3 of the constitution.
The government rejected the demand, saying Section 3 does not allow any group of people to exercise the sovereign power of the people. The King shall exercise such power through parliament, the cabinet and the courts, it said.
In his speech to the protesters, Mr Suthep said since Ms Yingluck had ignored the PDRC's "order", the committee had therefore issued an "additional order" that protesters demonstrate peacefully against Shinawatra family members and cabinet members.
Police are also ordered by the PDRC to take legal action against Ms Yingluck and her cabinet on charges of insurrection, he said.
"The PDRC orders police officers to return to their normal duties," Mr Suthep said, setting them a 12-hour deadline to comply.
"The military is asked to deploy for security purpose at state offices instead," he said.
In an earlier speech, Mr Suthep said when the prime minister steps down, he would ask protesters to go home.
"Just wait for another three days. If this is not finished, people in the Shinawatra family won't find any happiness in their lives," he said.
According to Mr Suthep, the Shinawatra family should expect to be treated with contempt by people nationwide.
"If the prime minister doesn't want to be hated any more, do as we recommend," he said.
Mr Suthep again insisted the Yingluck administration had lost its legitimacy to stay in power since it had rejected the Constitution Court's ruling on the charter amendment to make the Senate a fully elected body.
"Various actions of this government led by Ms Yingluck intentionally violated the constitution. As a result, this government is illegitimate," he told protesters at the rally site in front of Government House.
He said the Yingluck administration could not even assume the role of a caretaker government.
"As a result the country is in a vacuum, making it possible to invoke Section 7 of the charter to establish an interim government to pursue national reforms."
Mr Suthep also criticised Ms Yingluck for her announcement of a House dissolution before it was royally endorsed.
He said such an act was considered offensive to the monarchy.
The United Front for Democracy against Dictatorship (UDD) on Tuesday called on the people to rise up against the PDRC, saying the group had committed brazen undemocratic acts.
The group said Mr Suthep was violating the charter and offending royal authority when he rejected the House dissolution and the calling of an election.
The UDD said that the Election Commission had the responsibility to organise the general election or it would risk violence and a possible civil war.
Early in the day, Ms Yingluck appeared on the verge of tears during a press conference at the Army Club and insisted she would not step down as caretaker prime minister until a new cabinet has been formed.
"I have retreated so far and I don't know where to retreat further," she said.
Ms Yingluck said there was nothing more she could do after dissolving the House. She would stop performing her duties as caretaker premier only when a new cabinet is officially appointed.
The prime minister became emotional when asked about the protesters' demand that her family leave the country.
"I am not without feelings. I have heard their calls. As for the one about my family, I am also Thai. Will there be no place for me here? Is this what is going to happen?
"I have taken steps back as far as I can. I am asking to be treated fairly," she said and abruptly left the press conference. She also called on the protesters to return home.
"Please stop the protest and use the election mechanism. With the royal decree [calling for the election] in place, the Thais who truly own the powers can take part and decide the government that they want. This is in line with peaceful means and the constitution," she said.
Mr Suthep responded last night and asked Ms Yingluck to treat the protesters fairly. He said the demonstrators were aware of their legal rights and had never "banished" her brother, Thaksin Shinawatra, or anyone from the country.
"Thaksin left not because the people drove him away. He fled.
"And the people here shout "Get out" not because they want you to leave the country. They want you out of the prime minister's post. Don't make such a false accusation," he said.
Mr Suthep also chided Ms Yingluck for saying that she could not take any more steps back to appease the protesters. Calling a general election was just a trick to regain power and allow corruption to carry on after the election, he alleged.
A video clip showing Ms Yingluck smiling shortly after appearing to be on the verge of tears went viral yesterday.
It showed Ms Yingluck turning and smiling to a reporter who called out to her after she left the podium, sparking arguments on social media over whether Ms Yingluck had pretended to cry.
However, a reporter who covered Ms Yingluck's press conference said she turned round and smiled to another reporter who had followed her and asked her a question.
Army chief Prayuth Chan-ocha dismissed a rumour that spread widely on Tuesday that he, together with former defence minister Gen Prawit Wongsuwon and former army chief Gen Anupong Paojinda, met Mr Suthep at a military base.
Gen Prayuth said he did not meet Mr Suthep while Gen Prawit was ill with a cold and stayed at his home in Lat Phrao and Gen Anupong was abroad.
Col Winthai Suwaree, deputy army spokesman, said Gen Prayuth remained concerned about the political situation.
"The army chief is not being passive, nor is he at ease, and he's trying to find ways to resolve the problem as quickly as possible," Col Winthai said.