Mr. Alward, like any Ontario resident, can get as much naloxone as he needs free from one of the more than 2,800 pharmacies that stock the medication in the province. The federal government made the drug available without a prescription in 2016, and Canada’s provinces have developed a range of approaches to delivering it to users. In Ontario, Canada’s most populous province, authorities began two years ago distributing it to drugstores and jails, and later expanded the program to include homeless shelters and drug-rehabilitation centers.

Canada serves as a model for those lobbying for similar access to naloxone in the U.S., where a patchwork of state laws governs the medication’s availability. The federal government has deemed naloxone a prescription drug, but the U.S. Food and Drug Administration began working two years ago on helping drugmakers develop an over-the-counter version.

Laura Thomas, interim state director in California for the Drug Policy Alliance, a New York-based group that advocates ending the so-called war on drugs, has called on the FDA to take quicker action on making the drug more available.

“If Canada can make it over-the-counter, the U.S. certainly could,” said Ms. Thomas, who says the drug is urgently needed to reduce the toll from opioids.

U.S. critics say widespread availability of naloxone could increase opioid use. Republican Maine Gov. Paul LePage has consistently vetoed legislation, most recently in April, to widen the drug’s availability in the state, where opioid abuse is widespread.

Giving addicts access to naloxone “produces a sense of normalcy and security around heroin use that serves only to perpetuate the cycle of addiction,” he wrote in a letter explaining one of his vetoes in 2016.

Mr. Alward acknowledged that some users try to push the limits of their high because they have access to the antidote and often to safe-injection sites where they can expect to be treated if they overdose. But he said he was thankful the medication saved his life and others’.

Mr. Alward said he has used the antidote 28 times on people who overdosed.

“When you’re watching somebody die in front of you, time seems like it’s flying by,” said Mr. Alward, whose tattooed forearms are pocked with injection scars from years of drug use. “You have to slow down if you’re going to save them.”

Those injected with the medication are often breathing and back up within minutes. They then suffer intense withdrawal symptoms, including vomiting and muscle aches. Opioids don’t work as long as naloxone remains in their systems.

Even with the antidote widely available, the death rate from opioid overdose continues to skyrocket in Canada. The country is second only to the U.S. in per-capita use of opioids, which include fentanyl, oxycodone, heroin and morphine. Fentanyl is 50 to 100 times stronger than heroin, and users often misjudge its strength when injecting the drug, leading to overdoses.

More than 10 people a day died from opioid overdoses last year, according to Canadian government statistics, an almost 40% increase from 2016, when slightly more than 7 people died a day.

In the U.S., which has 10 times Canada’s population, an average of more than 115 people a day died in 2016 from opioids, according to the Centers for Disease Control and Prevention.

Advocates and officials in Canada acknowledge that naloxone itself won’t stop the spread of abuse of powerful street drugs. The medication is one prong in a so-called harm-reduction approach, adopted by the cities of Vancouver and Toronto, that also includes creating safe places for addicts to inject, offering sophisticated rehabilitation programs, and even advocating for decriminalization.

Before Canada’s federal government changed the law two years ago, naloxone was a prescription drug. Many users felt stigmatized when they went to the pharmacies to get kits, limiting the medication’s reach onto the street, said Zoe Dodd, a Toronto community worker and activist.

Ms. Dodd helped set up the city’s first overdose-prevention site last year on the edge of the rundown Moss Park area in Toronto. The activists’ safe-injection effort was illegal at the time, but since then the province has created similar sites.

Before 2016, Ms. Dodd said, she collected as much free naloxone as she could when it was handed out at harm-reduction conferences in the U.S. She and other activists also worked with U.S. activists to create an “underground railroad” to ship crates of the medication north. Activists distributed naloxone to users and set up workshops in major Canadian cities to teach people how to recognize overdose symptoms and how to administer the drug.

“If people weren’t sharing that knowledge, a lot more people would be dead in this city,” Ms. Dodd said.

Since 2016, Ontario has handed out more than 100,000 naloxone kits to prisons, homeless shelters, community centers and pharmacies. The black zippered cases contain two vials of the medication, two syringes, latex gloves, a mask to protect resuscitators and instructions.

Maria Zhang, a pharmacist and educator at Toronto’s Centre for Addiction and Mental Health and the University of Toronto, said the hospital staff were so eager to offer naloxone that they bought pencil cases in bulk and jury-rigged their own kits to hand out before the province’s supply became widely available.

The provincial pharmacy program has cost 6.5 million Canadian dollars ($4.9 million) over two years, including the cost of the kits as well as professional and training fees paid to pharmacies.

A recent study by researchers at the University of British Columbia in Vancouver found that naloxone prevented the deaths of 226 people in 2016, when the province’s coroner recorded more than 667 deaths from fentanyl.

Judy Darcy, British Columbia’s minister of mental health and addictions, said arguments about naloxone serving as an enabler pale in the face of the metastasizing crisis.

“It’s pretty basic,” she said. “People need to be alive in order to get onto a pathway to treatment.”

Write to Vipal Monga at vipal.monga@wsj.com