Murdered Russian opposition leader Boris Nemtsov

US Secretary of State John Kerry on Sunday urged Russia to carry out a "thorough, transparent, real investigation" into the murder of Russian opposition leader Boris Nemtsov, a fierce critic of President Vladimir Putin.

Nemtsov was shot dead in Moscow on Friday, just two days before he was to have led a major opposition rally against the government.

"The bottom line is that we hope there will be a thorough, transparent, real investigation not just who actually fired the shots, but who if anyone may have ordered or instructed this or been behind this," said Kerry, speaking to ABC television's "This Week" program.

"Our hearts go out to the Russian people," he said. "This was a man who was deeply committed to a better relationship with the world."

Police and investigators in Russia said Nemtsov was shot down by unidentified assailants as he was walking with a woman along a bridge not far from the Kremlin.

President Barack Obama late Saturday condemned what he called Nemtsov's "brutal" and "vicious" murder, and praised the opposition leader as a "tireless advocate for his country, seeking for his fellow Russian citizens the rights to which all people are entitled."