More than 70,000 people marched through central Moscow on Sunday in memory of opposition leader Boris Nemtsov who was gunned down near the Kremlin in the highest-profile assassination of Vladimir Putin's rule, organizers said.

"We believe that more than 70,000 have turned up," one of the organizers, Alexander Ryklin, told AFP, adding that many people had yet to exit the underground railway network. Police estimated the crowd at more than 16,000.

Families, the old and young walked slowly, with many carrying portraits of Nemtsov, an opposition politician and former deputy prime minister who was shot dead while walking home from a restaurant in central Moscow on Friday night.

His murder has prompted deep soul searching in a country where for years after the Soviet Union collapsed.

Putin has vowed to pursue those who killed Nemtsov, calling the murder a "provocation."

National investigators who answer to the Russian leader say they are pursuing several lines of inquiry, including the possibility that Nemtsov, a Jew, was killed by radical Islamists or that the opposition killed him to blacken Putin's name.

Putin's opponents say such suggestions show the cynicism of Russia's leaders as they whip up nationalism, hatred and anti-Western hysteria to rally support for his policies on Ukraine and deflect blame for an economic crisis.

Some Muscovites, accepting a line repeated by state media, appear to agree that the opposition, struggling to make an impact after a clampdown on dissent in Putin's third spell as president, might have killed one of their own.

Ukrainian President Petro Poroshenko said Nemtsov had told him about two weeks ago that he planned to publish evidence of Russian involvement in Ukraine's separatist conflict.