(Adds quotes, Rosneft comment, Sistema share price, background)
XIAMEN, China, Sept 5 (Reuters) - Shares in Russian industrial conglomerate Sistema jumped 15 percent on Tuesday after President Vladimir Putin said he hoped it would reach an out-of-court settlement in its dispute with state oil giant Rosneft.
A Russian court ruled last month that Sistema should pay 136.3 billion roubles ($2.4 billion) in damages to Rosneft to settle a dispute over mid-sized oil producer Bashneft. Sistema has said it will appeal against that decision.
Putin, speaking at a news conference after a summit in China, said he had met Rosneft CEO Igor Sechin as well as Vladimir Yevtushenkov, chairman and main owner of Sistema, and listened to their positions.
"It would be wrong for me to publicly announce my position. I hope that they will be able to reach an amicable agreement," Putin told reporters.
"It would benefit both companies and the Russian economy as a whole," he said, adding he had given no direct instructions to any party in the case.
A Rosneft spokesman said the company had not received any "amicable" proposals from Sistema. Sistema did not immediately respond to a request for comment.
Shares in Sistema were 7.89 percent higher at 13,535 roubles on the Moscow Exchange by 0816 GMT, having jumped 15 percent to their highest since June 20 immediately after Putin's comments. The broader market index was up 0.21 percent.
In June, Kremlin spokesman Dmitry Peskov said Putin would not intervene in the row after the court froze more than 170 billion roubles worth of Sistema assets as part of the litigation.
The case has rekindled broader fears about investor rights in Russia. Sistema has rejected Rosneft's claims as groundless and said the case was hurting the country's investment climate. (Additional reporting and writing by Vladimir Soldatkin and Maria Kiselyova; Editing by Jack Stubbs and Mark Potter)