Uthai Yodmanee, leader of the Network of Students and People for Reform of Thailand, said Tuesday the demonstrators would move only if the intersection became unsafe.
Mr Uthai was responding to a police request for protesters to relocate to the nearby Supachalasai Stadium.
He said the only safe rally sites he could think of were the Royal Thai Police Office or the city police headquarters.
If more people join the protest at Uruphong, the rally space will expand. But it will not require closing off adjacent roads, Mr Uthai said.
If and when the Internal Security Act (ISA) is lifted, the protesters would consider returning to Government House, he added.
The protesters earlier agreed to move away from Government House to allow for the visit of Chinese premier Li Keqiang.
They have vowed not to disperse even if the government extends the ISA _ imposed in Dusit, Phra Nakhon and Pomprap Sattruphai districts until Friday _ to also cover Uruphong.
The protesters were considering asking Prime Minister Yingluck Shinawatra to review the role of city police chief Khamronwit Thoopkrajang in handling the protest, Mr Uthai said.
National Security Council chief Paradorn Pattanatabut said the Centre for the Administration of Peace and Order and security agencies will today meet to consider whether the ISA's coverage should be expanded.
Lt Gen Paradorn said the number of protesters has doubled from about 400-500 since they first gathered at Uruphong.
Deputy secretary-general to the prime minister Suporn Atthawong claimed security authorities had found the protest was backed by local politicians, particularly Bangkok councillors and district councillors. He did not provide any evidence to back the claim.
Opposition chief whip Jurin Laksanavisit denied the Democrat Party is allied with the protest. People came to the rally because of the government's poor performance, he said.
He questioned the invocation of the ISA, which he said is a costly exercise.
Many people could not tolerate the government's administrative failures, Mr Jurin said.
The Democrat executive blasted the government for paying too little attention to addressing the rising cost of living. The prime minister was too busy taking overseas trips to focus on domestic issues, while her government was too busy amending the constitution and issuing a political amnesty law, he added.
The cabinet yesterday agreed to keep the ISA in force until Friday, as proposed by Deputy Prime Minister Pracha Promnok.
Pol Gen Pracha told the cabinet the ISA is still necessary to contain the protest at Uruphong intersection.
Meanwhile, the Office of the Vocational Education Commission (Ovec) consulted 28 government vocational colleges in Bangkok yesterday after some vocational students were found to be taking part in the Uruphong rally.
Ovec secretary-general Chaiyapruek Serirak said students are free to join the protest if they wish.
"The constitution clearly says that a person has the liberty to assemble peacefully and without arms, so students are not prohibited from joining the rally," he said.
Vocational colleges will not get involved in any political conflict and teachers have no responsibility to take care of their students at the rally, he added.
Mr Chaiyapruek said all colleges have been asked to keep an eye on their students. They should also ensure the students' education is not adversely affected by their participation in the protest.