* Russian rouble, assets slightly recover from huge selloffs
Kremlin, central bank sought to calm down markets
* Russian bonds hit by new proposal for sovereign debt curb (Adds details, quotes, background)
By Katya Golubkova
MOSCOW, April 10 (Reuters) - The Russian rouble slightly recovered on Tuesday from heavy losses earlier in the day and on Monday, trading down by more than 2 percent as investors continued a sell-off amid a new round of U.S. sanctions.
It was the second straight day of losses for the Russian currency following fresh U.S. sanctions imposed on some of Russian oligarchs and their assets.
At 0856 GMT, the rouble was 2.3 percent weaker against the dollar at 62.08 - still its lowest since December 2016 - and had lost 2.4 percent to trade at 76.50 versus the euro.
Rising Brent oil prices, the benchmark for Moscow's flagship Urals oil pricing were up by 1.2 percent in early trading but did nothing to help a recovery for the rouble.
Apart from the fresh sanctions, the Russian market was under additional pressure from a proposal by two U.S. congressmen to impose sanctions on Russia over the poisoning of ex-spy Sergei Skripal and his daughter in Britain - allegations Moscow denies.
The bill, whose prospects remain unclear, calls for "prohibiting U.S. persons from engaging in transactions with, providing financing for, or in any other way dealing in Russian sovereign debt that is issued on or after the date that is 180 days after such date of imposition of sanctions."
Russian sovereign dollar bonds fell across the curve, with the 2043 issue tumbling 3.8 cents in the dollar to around 105.7 cents according to Tradeweb. Russian five-year credit default swaps rose to 144 bps, their highest since end-September.
"While the general backdrop remains uncertain and the threat of further sanctions is unclear, we believe the Russian market is near a temporary floor," Alfa Bank said in a note.
"We note that the fundamentals surrounding the Russian market remain mostly unchanged and that Russian equities still provide among the healthiest dividend returns globally. We would thus ignore the current jitters and buy into the current weakness, particularly with dividend season almost upon us."
Russian officials, including central bank governor Elvira Nabiullina and Economy Minister Maxim Oreshkin, sought to calm investors.
Nabiullina, who had to deal with a sharp rouble drop at the end of 2014 amid the first Western sanctions, told a forum that the central bank had a wide range of tools at its disposal with which to address the risks. No risks were seen for now to Russia's financial stability, she said.
Oreshkin told the same forum that the floating rouble rate was helping to offset a possible negative effect on the Russian economy. The economy is projected to grow by 2 percent this year after a 1.5 percent increase in 2017.
Despite the sell-off, some analysts said it was premature to begin to revise economic forecasts.
"We tend to believe that the impact on economic growth ought to be fairly limited given that Russia has already deleveraged, and economic policies of the recent years ensured stabilisation and de-risking of the domestic economy," Renaissance Capital analysts Oleg Kouzmin and Daniel Salter said in a note.
The dollar-denominated Russian stock index also recovered somewhat from more than 4 percent falls earlier the day, while the rouble stock index was on the rise.
The dollar-denominated RTS index was down by 1.7 percent overall to 1,076 points. The rouble-based MOEX Russian index was 1.5 percent higher at 2,122.3.
On Monday, the rouble suffered its biggest daily fall in more than three years and stocks in major Russian companies also slid, as investors reacted to a new round of U.S. sanctions targeting some of Russia's biggest tycoons.
The United States imposed sanctions on seven Russian oligarchs and some of their companies on Friday, including Viktor Vekselberg's Renova and Oleg Deripaska's En+ Group , Rusal and some other assets.
Rusal was trading down 2.5 percent after falling by over 5 percent earlier on Tuesday.
For a factbox on Russian oligarchs and officials on the fresh U.S. sanctions list, see.
For a factbox on Deripaska's debt, see.
For Russian equities guide, see
For Russian treasury bonds, see (Reporting by Katya Golubkova Additional reporting by Andrey Ostroukh, Elena Fabrichnaya, Maria Tsvetkova, Vladimir Abramov, Jack Stubbs and Tatiana Voronova in MOSCOW, Sujata Rao and Claire Milhench in LONDON Editing by Mark Heinrich)