The House of Commons passed a Canada-style Magnitsky bill Wednesday that will soon give Ottawa the power to sanction human-rights abusers around the world, prompting the Russian government to threaten tit-for-tat measures on Canadian officials when the legislation becomes law.

The House unanimously voted in favour of the bill Wednesday night, sending it to the Senate for final approval over the coming weeks. Although the legislation is named after Russian whistle-blower Sergei Magnitsky, who accused Russian officials of a massive tax-fraud regime before being beaten to death in a Moscow jail in 2009, it is meant to sanction human-rights abusers around the world. After months of threats in response to the legislation, Russia made its retaliation plan clear on Wednesday.

Read more: When it comes to Magnitsky laws, it's clear what Russia is looking for

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"We warn again that in case the pressure of the sanctions put on us increases … we will widen likewise the list of Canadian officials banned from entering Russia," Russian foreign ministry spokeswoman Maria Zakharova said in an Interfax news agency report.

"To a large extent, [the bill] simply copies the odious American 'Magnitsky Act' and is set to further undermine Russian-Canadian relations."

A number of Canadian officials, including Foreign Affairs Minister Chrystia Freeland, were banned from entering Russia in 2014 after Canada sanctioned members of Russian President Vladimir Putin's circle over the annexation of Crimea. Canada will become the fourth country to pass Magnitsky-style sanctions when Bill S-226 becomes law, following in the steps of the United States, Britain and Estonia. When the United States first passed the Magnitsky Act in 2012, Russia retaliated by banning Americans from adopting Russian children.

U.S.-born financier and anti-Putin campaigner Bill Browder has led the international effort to sanction human-rights abusers worldwide, in memory of Mr. Magnitsky, whom he hired as the lawyer for his Moscow-based Hermitage Capital Management hedge fund in 2005. Mr. Magnitsky was arrested in 2008 and died in prison in 2009 after accusing Russian officials of theft. Investigations by Russia's human-rights council eventually concluded he was beaten to death by prison staff.

"I'm gratified for Sergei's memory, for his wife, Natasha, for his son, Nikita, and for his mother, Natalya, that we finally have made this happen and that the Canadian people have honoured his sacrifice," Mr. Browder said.

Russia's reaction Thursday is the latest in a series of anti-Magnitsky legislation lobbying efforts by the government, its embassy in Ottawa and a Russian group in Canada. Over the summer, some members of Parliament received a letter from the Russian Congress of Canada calling on the government to withdraw its support for the Magnitsky bill. In the letter, President Igor Babalich said the legislation "will set a dangerous precedent of the Canadian government" and "further close the space for a dialogue with Russia at a time when Canada-Russia relations are already at a historic low."

Prior to his role with the congress, Mr. Babalich was a staff member of The Globe and Mail.

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It's not clear who will initially be targeted by the Magnitsky act, but a government official said on background that Russian names will likely be on the first sanctions list. Mr. Browder said he has provided Ottawa with evidence related to 282 individuals who he thinks could be sanctioned.

"We've now started supplying them with reams of evidence of people we believe should be subject to the Magnitsky act. We're starting with the people who killed Sergei Magnitsky," Mr. Browder said.

To date, 44 people have been sanctioned under the U.S. Magnitsky Act.

With files from Reuters