Speaking in Miramichi, N.B., the prime minister says Canadians expect his government to defend human rights.
Harper says Canada is not a country where people are jailed or killed for their political positions or for engaging in certain consensual acts between adults.
Earlier in the day, Foreign Affairs Minister John Baird also expressed hope that the controversy would be resolved before the Winter Games in Sochi begin in February.
The controversial Russian law bans so-called "propaganda of non-traditional sexual relations" and imposes fines on people who stage gay pride rallies.
Russia says it has no intention of changing the law as international pressure builds ahead of next year's Games.
"I think it's important to recognize there are some controversies in this matter, but the reality is that our position is that we don't imprison or kill people for acts committed freely between adults," Harper said.
"We don't imprison people for their expressing political positions. I think our position in this regard represents the position of Canadians and they expect that we speak in favour of these rights."
For his part, Baird expressed concern about what the anti-gay law will mean for Canadian athletes and spectators at the Games.
"We are concerned, obviously, about Canadian athletes and other participants, spectators and attendees of the Olympics there," Baird said during a conference call with journalists.
"But we should be very clear: they're only going to be there two or three weeks. The people of Russia will have to deal with this law 365 days of the year, every year. Let's hope that decency will prevail."
There have been calls for protests, a boycott and petitions to move the Games to Vancouver, where they were staged in 2010.
Baird, who is in Brazil on trade talks, says the furor over the law is a chance to put President Vladimir Putin's Russia under the microscope.
"We've got an important opportunity for the free world to be able to focus on what's happening in Russia in the recent weeks and months, and hopefully that can yield a change."
The foreign affairs minister also says he was pleased that the International Olympic Committee asked the Russian government to clarify parts of the law.
IOC President Jacques Rogge said Russia provided written re-assurances about the law on Thursday, but some parts remain unclear.
"We are waiting for the clarifications before having the final judgment on these reassurances," Rogge said.
U.S. President Barack Obama also spoke out against the law on Friday, saying he was deeply offended by it. He expressed hope that some gay and lesbian athletes will win some medals, something he said would "go a long way in rejecting the kind of attitudes that we're seeing there."
Russia's sports minister has said Olympians must respect the country's laws during the Sochi Games.
However, the Russian government says it will respect the private lives of Olympic athletes.
— With files from The Associated Press