The move followed the Constitution Court's ruling on Friday, which nullified the Feb 2 poll.
The secretary-general of the People's Democratic Reform Committee (PDRC) urged anti-government demonstrators to hold rallies in their provinces if they cannot come to join the demonstration in Bangkok.
The rally is to send a message that people need to see reform undertaken first before a new election is held, he said.
The demonstration in Bangkok next Saturday will begin at 9.30am at Lumpini Park, Mr Suthep said.
He promised a peaceful demonstration and urged 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.
Mr Suthep said that as a warm-up, he would lead marches on Bangkok streets from Monday to Friday to promote and build the momentum for the Saturday rally.