Time to Canuck the donuts.

Tim Hortons, the doughnut chain so popular in Canada that some hold it partly responsible for overburdening the nation’s socialized medical system, is opening its first outposts in the city Monday.

The Riese Organization is transforming its 13 Midtown Dunkin’ Donuts outlets into Hortons, providing new competition against the dominant doughnut maker — not to mention the city’s countless sidewalk morning-coffee carts.

There are some similarities — Dunkin’ has its “Munchkins” and Hortons has its “Timbits.”

But Hortons — named for the late hockey hall-of-famer who co-founded the chain — is also more of a restaurant, said Riese CEO Dennis Riese.

“Unlike Dunkin’ Donuts, Tim Hortons has a full-service kitchen and does all its baking on premises,” he said. “Business should be strong throughout the day, and not just during the morning rush.”

Riese said The Post deserves some credit for bringing the chain’s first outposts to the city.

In 1998, The Post ran a story — with the Page 1 headline “Under Mouse Arrest” — and photos of mice chowing down on the racks of one of Riese’s Dunkin’ locations. As a result, the chain sued him.

The legal battle over the sanitary conditions at the Midtown locations — which Riese insists “were never any worse than at any other Dunkin’ Donuts,” went on for years.

“It got really heavy-handed — they acted as if no other Dunkin’ Donuts ever had a mouse run through it,” he said

The two sides settled five years ago. In return for extending his franchise agreement to this month, Dunkin’ waived the noncompete agreement Riese had signed.

That allowed him to transform his Dunkin’ locations into those of the chain’s fierce rival.

Hortons has 3,400 locations, including 500 in the United States. Until now, the Hortons outlet nearest the city was in Connecticut.

Dunkin’, meanwhile, now has more than 400 Big Apple outlets. But Riese has claim to some of the highest-volume locations, in Times and Herald squares.

In recent years, coffee has been in the front lines of the battle among Dunkin’, Starbucks and McDonald’s, and Riese says he expects Hortons to lure many java junkies from the rivals.

jeremy.olshan@nypost.com