Suthep Thaugsuban said the meeting had been held under the auspices of the military and there was no compromise.
He did not say what action would follow if the ultimatum were not heeded.
On the eighth day of action to unseat PM Yingluck Shinawatra, police fended off protesters who descended on key sites in Bangkok. Four people have died in the unrest.
Dozens have been injured.
The protesters had declared Sunday the decisive “V-Day” of what they termed a “people’s coup”.
They say Yingluck Shinawatra’s administration is controlled by her brother, exiled ex-leader Thaksin Shinawatra, and they want to replace it with a “People’s Council”.
Suthep Thaugsuban said he had met the prime minister in a secret location in the presence of the army, navy and air force commanders.
“There was no negotiation and no compromise,” Suthep Thaugsuban was quoted as saying.
“I told Yingluck that this is the only and last time I see her until power is handed over to the people.
“There will be no bargaining and it must be finished in two days.”
Some 30,000 protesters had gathered earlier at about eight sites, police said, including Government House, television stations and the police headquarters.
Protesters did enter several TV stations to ensure a message from Suthep Thaugsuban was aired. It was broadcast by almost all of Thailand’s channels.
Suthep Thaugsuban called a general strike for government employees for Monday.
Yingluck Shinawatra had intended to give media interviews on Sunday at a Bangkok police complex but was forced to leave when protesters tried to break in.
Deputy PM Pracha Promnok urged people in the capital to stay indoors from 22:00 to 05:00 local time “so they will not become victims of provocateurs”.
The worst violence occurred when students attacked vehicles bringing pro-government activists to a Bangkok stadium on Saturday.
WkH83kTxzwsThe US House Ethics Committee has voted to release its report on former Republican Representative…
ABC News has agreed to pay $15 million to President-elect Donald Trump to settle a…
South Korea’s parliament has voted to impeach President Yoon Suk Yeol over his failed attempt…
Israeli war planes have carried out more than 100 air strikes in Syria on December…
President-elect Donald Trump has threatened to impose 100% tariffs on the BRICS countries if they…
Syrian troops have withdrawn from the city of Aleppo following an offensive by rebels opposed…