The demonstrators were vowing to defy the request from Melcor, the property development company that owns the park, to take their tents down and be out by Sunday at 11 p.m.
But instead of making arrests or issuing tickets, police were hoping the two sides would settle the issue without confrontation, said Acting Inspector Graham Hogg, who added police were even offering to seek the help of a mediator.
"We've taken a position from the outset that we'd like a positive, negotiated settlement," Hogg said on Sunday.
"Thus far, Melcor is in agreement with our strategy. Obviously, they would like them out sooner rather than later."
The news was greeted warmly by the Occupy protesters, who were gathered in an army-style tent that was heated by woodstoves that sheltered them from the -20 C weather on Sunday.
"It's definitely a relief but we know we're not out of the woods yet," said Mike Hudema, a spokesman with the protesters.
Hudema said about 20 to 30 people have been camping in the park. At night, many of them sleep together in the tent that has the stoves.
It isn't the first time Melcor has asked the demonstrators to leave. The company previously demanded they vacate the park late last month, but relented, saying they could stay as long as they were responsible and remained peaceful.
On Saturday, Melcor president Ralph Young expressed concerns in a letter to the protesters that their tents, which also include a teepee, were becoming more permanent. He said there were further safety concerns when a snowstorm hit Edmonton on Thursday and temperatures plummeted.
"Melcor, Occupy Edmonton leaders, and anyone associated with the failure to respond to real risks to human safety could face serious consequences should any actual damage or injury or death occur on the site," Young stated in the letter.
Edmonton police said Saturday that they had asked Occupy organizers to monitor everyone at the site every 15 minutes. Officers were worried about the frigid temperatures and the risk of carbon monoxide poisoning from heaters in tents.
Occupy Edmonton replied that its wood stoves have been approved by fire inspectors, and that it has fire extinguishers, smoke and CO2 detectors to further ensure safety.
Hogg said Edmonton police hope to avoid the sort of confrontations that have happened with Occupy protests in other cities.
Police in Victoria say most Occupy protesters obeyed a court order to leave the B.C. capital's Centennial Square Saturday morning.
Protesters in Vancouver have been told they must dismantle their camp by Monday afternoon.
And an Ontario judge is expected to rule Monday morning on the City of Toronto's application for a court order for protesters to vacate a downtown park.
In Edmonton, Hudema said it's important that the protesters be allowed to remain uninterrupted.
"This isn't like any other protest. The reason for the ongoing occupation is so that people can come together," he said.
"We want to eliminate corporate influence."
Also on HuffPost