The move followed the Constitution Court's ruling yesterday, which nullified the February 2 poll results.
Suthep, a former opposition Democrat Party MP, is the secretary-general of the People's Democratic Reform Committee (PDRC), the frontline anti-government protest group.
He urged anti-government demonstrators to hold rallies in their provinces if they were not able to join the demonstrations in Bangkok. He promised peaceful demonstrations and appealed for a big turnout to show the force of reform supporters.
The rally had originally been planned on March 30 but the date was moved a day forward to avoid disturbing the Senate election.
Suthep said that as a warm-up, he would lead marches on Bangkok streetsfrom Monday to Friday to promote and build the momentum for the Saturday rally.
Also today, opposition Democrat Party leader Abhisit Vejjajiva urged embattled Premier Yingluck and Suthep to hold talks to reach a common ground for holding elections, as the political impasse continues to plague the country.
"I don't know why Yingluck (Shinawatra) and Suthep (Thaugsuban) cannot hold talks together. It's time for both to stop demanding any conditions," he said.
Abhisit suggested that Yingluckand Suthep should decide together what should be done before a new election is held, otherwise there would be no guarantee that the next poll would be conducted successfully.
He said that the Election Commission (EC) and the government should hold talks with all parties.
The country's Constitutional Court had ruled yesterday that the general elections which were held on February 2 were invalid as polls had not been held in 28 provinces.
Thailand has been in political turmoil since mass rallies began in November with protesters demanding an un-elected People's Council to replace Yingluck's government.
The protesters accuse Yingluck of acting as a proxy for her fugitive brother, former premier Thaksin Shinawatra, who was ousted in a coup in 2006. He lives in self-exile in Dubai to escape a jail term on a corruption conviction.