A woman told the BBC by phone crowds were still large late on Monday.
A human rights campaigner said security forces loyal to President Bashar al-Assad had fired shots at the protesters, reports said.
Syria's interior ministry has said the unrest amounts to armed insurrection.
Earlier, funerals were held for some of those killed in Sunday's violence in the city, with crowds calling for the end of Mr Assad's rule.
Eight people died in Homs on Sunday after soldiers fired on crowds protesting at the death of a tribal leader in state custody.
The opposition says the occupation of the city centre will continue until their political demands are met. These include the immediate lifting of Syria's longstanding emergency laws and the release of political prisoners.
Activists say that checkpoints have been set up around the square to ensure that people coming in are unarmed civilians.
One opposition supporter, who said his brother was shot dead in Sunday's protests, said volunteers were providing the demonstrators with food and water.
Another, Najati Tayyara, told AFP news agency: "More than 20,000 people are taking part in the sit-in at Al-Saa Square and we have renamed it Tahrir Square like the one in Cairo.
"It is an open-ended sit-in which will continue until all our demands are satisfied."
A human rights campaigner, who is in contact with the protesters, told Reuters that a member of the security forces had ordered them to leave, before the forces opened fire and used tear gas.
At least one person was injured, according to the activist.
Two residents of Homs also said they heard gunfire in the area near the square, Reuters reported.
The unprecedented wave of protests in Syria shows no sign of abating, despite promises of reform by President Assad, says the BBC's Kim Ghattas.
Syria's official news agency has also been reporting on events in Homs. It said three army officers including a brigadier-general, together with his two sons and a nephew, were ambushed and killed on Sunday by "armed criminal gangs" which then mutilated the bodies with sharp tools.
The northern town of Banias also saw anti-government protests on Sunday.
In a statement, the interior ministry said: "The course of the previous events... have revealed that they are an armed insurrection by armed groups belonging to Salafist organisations, especially in Homs and Banias."
The BBC's Lina Sinjab says using the Salafist allegation is seen as a threat to peaceful protests.
Many fear it means further violence by authorities against protesters under the pretext of fighting terrorist elements, our correspondent says.
Meanwhile, the US said it was "very concerned" about Syria's response to protests.
State department spokesperson Mark Toner said Mr Assad was facing "a push by his very own people to move in a more democratic direction," and said the government "needs to address the legitimate aspirations of its people".
His comments came after a report by the Washington Post on Monday, citing classified US diplomatic cables, suggesting the US were covertly funding London-based Syrian opposition group Movement for Justice and Development. The US has denied the claims.
President Assad has recently promised reforms, including the removal of the country's 48-year-old emergency law, but protesters say the concessions are not enough.
Human rights groups say at least 200 protesters have been killed in the past four weeks as security forces try to quell the most serious challenge to Mr Assad's rule since he succeeded his father, Hafaz al-Assad, 11 years ago.