But the prospect of that succeeding, or any other attempt to sway Russia, appeared doomed by deteriorating relations between Washington and the Kremlin over accusations that Moscow was supplying attack helicopters to its longtime ally in Damascus.
Harper singled out Russia by name during question period in the House of Commons on Wednesday, urging it to join in the international effort to impose binding sanctions on the Assad regime.
Canada has been attempting to persuade Russia to stop supporting its Middle East ally as part of a broader effort led by the Obama administration.
Russia, a permanent member of the UN Security Council, has opposed any use of force to remove Assad, or any resolutions on sanctions. Opposition groups say 13,000 people have been killed in the 15-month Syrian uprising.
"We encourage Russia and others to join with us to apply binding sanctions against what is a murderous regime," Harper said, calling the Syrian situation unacceptable to Canadians and the international community.
Harper also appeared to be referring to China, the other permanent member of the security council that has backed Syria.
Harper spoke in response to a question by NDP Leader Tom Mulcair, who asked the prime minister specifically about diplomatic attempts to sway Russia.
"We have all witnessed the horrors in Syria with the Assad regime, where innocent children are now being targeted," Mulcair said.
"Canadians feel the pain of the Syrian people."
A UN report released earlier this week accused Syria government forces and their militias of abusing children as young as nine. It accused them of killing and maiming, arbitrary arrest, detention, torture, and sexual violence, and using children as human shields.
U.S. Secretary of State Hillary Clinton warned this week that the Syrian conflict could escalate dramatically because Russia is sending attack helicopters to Syria for use by the Assad regime.
Russian Foreign Minister Sergey Lavrov denied the claim Wednesday.
Clinton fired back, accusing Russia of risking "vital interests in the region and relationships" by blocking an international plan to take Assad out of power.
Foreign Affairs Minister John Baird was planning his own telephone call to Lavrov, but as of late Wednesday afternoon it had yet to happen. Baird has already met with Russia's ambassador to Canada to press the case for Assad to step down.
And last week, International Trade Minister Ed Fast delivered that message to Russian officials during a trade mission. The Russians held firm, telling Fast the calls for Assad's ouster were simplistic, didn't take into account the Syrian power structure, and would ultimately lead to greater chaos.
The fighting intensified in Syria as government forces reportedly took back a rebel-held area near the Mediterranean coast.
France's new Foreign Minister Laurent Fabius branded the situation a "civil war" and did what his Canadian counterpart has done on numerous occasions — called on Assad to step down.
"For more than a year the UN Security Council has dithered, while a human rights crisis unfolded in Syria. It must now break the impasse and take concrete action to end to these violations and to hold to account those responsible," said Donatella Rovera, the senior crisis adviser for Amnesty International, which released a scathing report on Syria.
The report documented unlawful killings, torture, arbitrary detention and the destruction of homes by government forces and militias. It was researched during a clandestine six-week foray into 23 Syrian towns and villages, and based on 200 interviews.
"Everywhere I went, I met distraught residents who asked why the world is standing by and doing nothing," said Rovera.