At 1220 GMT, the dollar-denominated RTS index <.IRTS> was up 1.7 percent at 989 points, while the rouble-based MICEX <.MCX> gained 1.4 percent to 1,995 points. Both indexes had opened over 1 percent weaker.
Among Russian blue chips, sanctioned firms Sberbank (>> Sberbank Rossii PAO) and Rosneft (>> NK Rosneft' PAO) rose by 2.2 percent and 1.2 percent, respectively. Russian gold miner Polymetal
On global markets the dollar and stocks fell on the U.S. election result, which prompted some investors to dump riskier assets.
Trump, who unexpectedly defeated Democrat Hillary Clinton, was widely seen as being more favourably disposed towards Russia than Clinton after making warm comments about President Vladimir Putin.
"Trump has been too contradictory to be sure, but clearly the chances of sanctions being lifted on Russia have risen substantially, which would improve the investment climate for Russia," said Charles Robertson, global chief economist for Renaissance Capital.
On Wednesday, Putin said Russia was ready to do its part to fully restore ties with Washington. Under the Obama administration Russia and the United States have clashed over the conflicts in Ukraine and Syria.
The rouble traded stronger as Wednesday progressed, but moves were more muted than in stocks.
At 1220 GMT the Russian currency was 0.4 percent firmer against the dollar at 63.53
Early on Wednesday on the interbank market the rouble briefly hit its weakest since Sept. 20 against the dollar as the reaction to an approaching Trump victory was initially one of risk aversion
Brent crude oil
Currency traders said the rouble was performing better than emerging-market peers because Trump was seen as being less hawkish on Russia than Clinton.
Tom Levinson, chief FX and rates strategist at Sberbank CIB, said the rouble was relatively insulated versus other emerging markets as Russia did not have a large current account deficit and was not that exposed to the United States in terms of trade.
"Hopes of improved political dialogue between the U.S. and Russia are for now overpowering any concern about how Trump's anti-trade stance will damage global growth and the oil outlook," Levinson said.
"If Trump is successful in reassuring markets then it's back to carry trades, and the rouble is the best," he said. Investors have been investing in Russian assets because of the higher returns they can offer than ones on developed markets in so-called "carry trades".
For rouble poll data see reuters://realtime/verb=Open/url=cpurl://apps.cp./Apps/fx-polls?RIC=RUB=
For Russian equities guide see
For Russian treasury bonds see <0#RUTSY=MM>
Russia in graphics: http://link.reuters.com/dun63s
(Additional reporting by Vladimir Abramov; Editing by Christian Lowe)
By Alexander Winning and Andrey Ostroukh