The Ontario Coalition Against Poverty came to Tory's office after two homeless men were found dead in less than 24 hours, with exposure to freezing temperatures believed to have played a role in both deaths.
"This shouldn't be the way we learn about homelessness," said Barrick German, a protester who said he's waiting to speak to the mayor.
When the city issues an alert, it automatically opens up emergency beds at city shelters.
OCAP members, including leader John Clarke, say the shelters are full, and those emergency beds are desperately needed.
They say they will stay in Tory's office until he comes out to speak to them.
Members of the police attended the protest, but remained some distance away from the demonstration.
"The death of anyone on the streets of Toronto — any single person, ever — is one too many," said Tory when asked about the shelters earlier on Tuesday. "We have to redouble our efforts."
Temperatures reached a low of -14 C overnight with a wind chill around -18 C. But the Toronto medical officer of health only issues the alerts when overnight temperatures reach -15 C or colder.
So far, the city has not issued an extreme cold weather alert.
Tory said there are clear protocols for cold weather alerts, but that he would follow up with medical officer.
On Tuesday afternoon, a Tory spokesperson said the mayor had asked the city manager to open warming centres. That was expected to happen immediately.