* Rouble posts sharpest one-day gain vs dollar since 2016 * Russian stocks, government bonds rally * Rouble, stocks price in lower uncertainty post U.S. vote * Higher oil prices buttress Russian assets (Adds detail, chart, quotes, updates prices) MOSCOW, Nov 5 (Reuters) - The Russian rouble posted its biggest one-day rise against the dollar in nearly four years on Thursday, pricing in higher oil prices and Democratic challenger Joe Biden edging closer to victory in the U.S. presidential election. The rouble, which reached its weakest level since March against the dollar on Monday at 80.95, had already recovered some ground, despite the rising number of coronavirus cases at home that fueled concerns about possible lockdowns. By 1518 GMT on Thursday it had made its sharpest single-day advance against the greenback since November 2016, gaining 2.8% from Tuesday’s close to 77.10, a level last seen on Oct. 27. Compared with levels for the rouble on global markets on Wednesday, when the Moscow Exchange was closed, the Russian currency was up 0.5% on the day. The rouble’s recovery “puts the Russian currency closer to fair value, which we see in the 70-75 range, assuming stable oil prices and foreign politics,” ING said in a note. Russian bonds also welcomed signs of progress in the U.S. election. Yields on 10-year benchmark OFZs, which move inversely with prices, fell to their lowest level since mid-August of 5.94%, from 6.29% on the eve of the vote. For weeks, the rouble has been under pressure over fears of more sanctions against Moscow, something that some analysts said was possible should Biden win. Versus the euro, the rouble was up 1.9% on the day in Moscow at 91.12, moving away from 94.1425, its weakest level since late 2015, which it hit on Monday. In the next few weeks, the rouble will see a decline in state support as the finance ministry will cut its regular sales of foreign currency to 50.1 billion roubles ($648 million) in November, below the 120 billion roubles predicted by analysts in Reuters poll. Brent crude oil, a global benchmark for Russia’s main export, was up 0.5% at $41.40 a barrel, extending its rapid recovery of the past days above the $40 threshold. The dollar-denominated RTS index gained 5.7% to 1,171.6 points. The rouble-based MOEX Russian index was 2.9% higher at 2,867.5 points, its highest since early-October. ($1 = 77.3000 roubles)