Presidential candidate Tan Cheng Bock said he was "disturbed" by Tan Jee Say's comments about challenging the government as this could "create dissent" between the President and government.
He also criticised Tan Jee Say's rally on Tuesday night for "having thrown up suggestions not within the Constitution".
On Tuesday evening, the 57-year-old investment advisor said he wanted to change the direction of the Presidency to one that is closer to people's aspirations, including having the President challenging and checking on the government.
However, Dr Tan said, "We don't want to create dissent between the President and the government in power. We have to think in terms of Singapore first. If we start to have this problem, it's going to have to affect our whole country."
When it comes to bad policies or issues, the President can warn the government privately, he said, "I want to work closely with the government but it doesn't mean I become so weak and just toe the government line."
Dr Tan, speaking to reporters at Raffles City on Wednesday, revealed more details on his rally on Thursday evening.
Held at the Singapore Expo hall 8 from 7:30 pm to 10 pm, his line-up of speakers consists of a wide range of people, including professionals, taxi drivers and the youth. His 37-year-old son, Joshua, and his 40-year-old daughter, Ming Li, will be speaking as well.
He has selected 18 speakers but only some will speak. They have been reminded to discuss the President's powers only as as set out within the boundaries of the Constitution.
Dr Tan stressed that he will not have speakers from political parties, even though those from the People's Action Party and opposition parties have asked to speak at his rally.
A President cannot be proxy to any political party, he reiterated. "The day I'm a proxy to any political party, so PAP or SDP (Singapore Democratic Party), that will start on the wrong footing already," he said.
Dr Tan also shared that, when he first wanted to enter the race, some people wanted to support him but were worried about losing their job. They were working in the government or government-linked companies, while some were ex-PAP colleagues.
"We should not live in fear, we should all enjoy being able to express our views freely and openly, challenge each other on issues," said Dr Tan, adding that people must learn to accept differences in views.
Dr Tan's daughter Ming Li, who prefers to stay away from the public eye, was seated next to her father.
She said she agreed to speak for her father at his request. "He is the only candidate who can really unify the nation in spite of all the political diversity," she said, describing Dr Tan as "very warm".
"I will basically be giving a testimonial of my father, of growing up with him and witnessing the things that happened as he served the nation and his patients," she added.
"I'm very proud of him, very proud to be sitting beside him."