Boris Nemtsov had criticized Putin in a radio interview hours before he was murdered in Moscow last Friday.
The head of Russia’s Security Council accused the U.S. of funding Russian opposition groups.
Boris Nemtsov's allies have pledged to publish a report he was working on at the time of his death.
At least 17 deaths at a Ukraine coal mine Wednesday bring the 15-year death toll there to more than 300.
Before his death, Boris Nemtsov, a vocal critic of Putin, had been organizing an upcoming rally in protest of the conflict in eastern Ukraine.
Nemstov was respected in Russian politics, despite his views. Few other opposition leaders had the support he did.
Cameras were either turned off or failed to capture relevant footage when Russian opposition leader Boris Nemtsov was killed, reports say.
Anna Duritskaya, 23, is purported to be the lone witness to the Russian opposition leader's killing.
Inna Duritskaya also claimed that Russian President Vladimir Putin is trying to link the murder to the conflict in eastern Ukraine.
Last week, Kerry had accused Russia of lying about its role in the conflict in eastern Ukraine, which has so far claimed 6,000 lives.
Marchers blame Kremlin for the shooting death of the opposition leader.
The former Soviet country is likely to release official results Monday.
The opposition politician was shot four times as he walked in Moscow.
The creator of the Internet is offering a cool sum to anyone who can build a top-notch surveillance system that operates at -85 degrees Fahrenheit.
The event will replace a planned protest march Nemtsov had supported before he was shot and killed Friday.
Ukrainian President Petro Poroshenko said in televised remarks Saturday Boris Nemtsov told him he had proof of Russia's role in the Ukraine conflict and would reveal it.
The senior U.S. senator in Arizona has long been a critic of the Russian president, having previously accused him of "literally getting away with murder."
The U.S. government called for a prompt investigation into the killing of opposition leader Boris Nemtsov, who was shot dead in Moscow on Friday.
Boris Nemtsov had been due to lead a mass rally against Putin and the war in Ukraine this Sunday.
An unidentified attacker shot Nemtsov, 55, four times while he was walking near the Kremlin.
Around a quarter of Russian respondents said Russia shouldn't act if the U.S. provides weapons to Ukraine.
Amid sanctions, food prices in Russia are rising.