* Putin meets companies, says amicable solution desirable
* Sistema shares rise 15 pct to highest in three months
* Sistema considers Putin remark "guidance" (Adds Sistema and analyst comment, court turning down Sistema request to unfreeze assets, updates share price)
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.
Putin said on Tuesday he had met Rosneft Chief Executive Igor Sechin as well as Vladimir Yevtushenkov, chairman and main owner of Sistema, and that an amicable agreement would benefit both companies and the Russian economy as a whole.
Shares in Sistema jumped 15 percent on the Moscow exchange to their highest since June 20 after Putin's comments. In June, the Kremlin said Putin would not intervene in the row over mid-sized oil producer Bashneft.
"We agree with the president and take his words as a guide for action. We had already offered to the claimants to come to the negotiating table and to invite independent experts," Sistema CEO Mikhail Shamolin said.
A spokesman for Rosneft said the oil firm "had never received any peaceful proposals from Sistema".
A court in the Russian region of Bashkortostan ruled last month that Sistema should pay Rosneft 136.3 billion roubles ($2.4 billion) to settle the claim that Rosneft-controlled oil producer Bashneft was stripped of assets when Sistema was the owner.
Sistema has rejected the claim as groundless and said it would appeal against the court decision. It has appealed against asset freezes imposed as part of the litigation but its latest request was turned down by a court on Tuesday.
Shares in Sistema hit 14.45 roubles shortly after Putin's comments but pared some of the gains to close the main session 8.77 percent higher at 13.6 roubles apiece.
"If the Russian president's hopes materialise, and the payout under an amicable settlement is less than implied by the existing court order, Sistema's debt burden will be lower," analysts at Raiffeisenbank wrote in a note.
"However, so far the likelihood of an amicable agreement is not that high, given that Rosneft is contesting the court decision," they added.
Rosneft had sought more than 170 billion roubles in damages and said it would contest the court decision to order Sistema pay less.
The dispute has rekindled broader fears about investor rights in Russia. Sistema said the case was hurting the investment climate.
Putin, speaking in Xiamen, China, said he had given no direct instructions to any side in the case. ($1 = 57.3098 roubles) (Additional reporting by Vladimir Soldatkin; Editing by Dale Hudson)