He also suggested that the province would keep opening and closing again if there are spikes in cases.
The premier argued that the course of the pandemic and the government's response depends on young people.
Editor's Choice: Legault Explained Why Schools In Quebec's Red Zones Are Staying Open
If we want to limit deaths, the solution is in your hands.
Premier François Legault
"We could have a nice summer because in the spring efforts were made by young people to reduce contacts."
The premier said it's possible we could find ourselves again in the position we're in now, with cases rising and significant community transmission.
"As long as we don't have a vaccine, there's a possibility for two waves, three waves, four waves."
"The only thing we can do," he said, "is to say, 'ok, we're opening a bit and if the number of cases rises too quickly, we'll close a bit.'"
But he admitted the government is limited in its ability to control transmission without public collaboration, especially that of young people. He called on them to follow the rules for the sake of all Quebecers.
"Now you have a new challenge: 28 days with minimal contacts. I know you can do it. I'm counting on you all."