MOSCOW (Reuters) - Now may be the time to invest in Russian shares because oil prices have hit bottom and the Russian stock market is rising, veteran U.S. financier Jim Rogers said on Monday.

“I’m very optimistic about the future of Russia,” he told a conference in Moscow arranged by investment firm BCS. “Certainly one of the most attractive stock markets in the world these days for me is Russia.”

The dollar-denominated RTS index .IRTS of Russian stocks fell by 45 percent last year as oil prices plunged and Western countries imposed sanctions over Russia's support of separatist rebels Ukraine. However, the RTS has gained 20 percent since the start of this year.

Rogers, who now lives in Singapore, has been a prominent financial commentator since the 1970s, when he founded the Quantum Fund in partnership with George Soros.

Russia could now be "the right place at the right time" for investors, he said. His own portfolio consists largely of Russian shares, he said, among them fertilizer company Phosagro PHOR.MM, airline Aeroflot AFLT.MM and the Moscow Exchange <MOEX.

The country’s economic downturn may make it an unlikely investment prospect, he said, but he was optimistic the stock market was going to rise more.

“Something has happened over in the Kremlin. The old ways of doing things in Russia have changed in my view,” he said.

Rogers said that his optimism towards the Russian market was connected with his view that international oil prices have reached their bottom.

He also recommended buying short-term Russian treasury bills for investors with a one-year horizon.