Navalny, one of President Vladimir Putin's most prominent critics, has separately complained of acute back and leg pain and accused authorities of refusing him access to his chosen doctor and of declining to supply him with the right medicine.
The legislation, which could pave the way for Putin to stay in power until 2036 should he choose to do so and win re-election, reflects sweeping changes to the constitution that were brought in last year.
In a readout of their telephone call, the Kremlin said the Saudi prince outlined initiatives to reduce greenhouse gas emissions and increasing the share of renewable energy sources in the Middle East.
Putin spoke of Russian efforts to protect the environment, the Kremlin said.
Russian assets have been under pressure since last week as markets prepared for a new round of US sanctions over alleged election meddling, which Moscow has denied.
The rouble gained 0.2% to 90.30 against the euro , hovering away from the 87 mark seen before the threat of new sanctions intensified.
"Vaccination, of course, is a voluntary decision for every person. It is every person's personal decision," Putin said at a televised government meeting on Monday about Russian vaccines against COVID-19. "By the way I plan to do this tomorrow."
"Today we can say confidently -- and practice indisputably confirms -- that Russian vaccines are absolutely reliable and safe," he said. "No other similar foreign drugs have shown such a high level of protection."
"The document prepared by the US intelligence community is another set of baseless accusations against our country for interfering in American domestic political processes," Russia's embassy in the United States said in a statement on Facebook.
Consumer regulator Rospotrebnadzor said earlier on Tuesday it had identified the first two cases in Russia of the new variant of the coronavirus first detected in South Africa.
In fact, trials have already been done in Russia and we can say with confidence that the (Sputnik V and EpiVacCoriona) vaccines registered in Russia also work against new strains.
Russia's federal budget could get a boost of more than 2 trillion roubles ($27 billion) from additional revenues this year if oil prices and the rouble exchange rate remain at current levels, the finance ministry said earlier on Thursday.