The long-running row over mid-sized oil company Bashneft pits powerful Rosneft chief executive Igor Sechin, a close ally of President Vladimir Putin, against billionaire Vladimir Yevtushenkov who told Russian media outlet RBC that the latest lawsuit was an "act of intimidation".
Yevtushenkov was placed under house arrest in 2014 over alleged money laundering before Moscow then renationalised Bashneft, saying its privatisation had been illegal, and dropped all charges against him.
Rosneft bought a controlling stake in Bashneft from the government in 2016. It subsequently alleged Sistema had removed assets from the company, something Sistema denies.
A Russian court ruled in August that Sistema should pay more than 136 billion roubles ($2.3 billion) to Rosneft in compensation as a result of this first lawsuit.
Thursday's legal move is a separate claim and news of the development drove Sistema's shares more than 17 percent lower, to below 10 roubles each, their lowest since the end of 2014.
"By pumping out groundless multi-billion lawsuits, Rosneft is just trying to compensate the costs of (buying) Bashneft, in other words, get the asset for free, at Sistema's expense," Sergei Kopytov, a spokesman for Sistema said.
Putin has fuelled speculation about the Kremlin's role in such disputes by calling on Rosneft and Sistema to settle their differences out of court, saying this would benefit both companies and the wider Russian economy.
But the president's intervention appears to have so far been ignored, with both companies accusing one another of not making compromise proposals, and the dispute has resurrected fears about the risk of doing business in Russia.
Putin's spokesman Dmitry Peskov said on Thursday it was up to the courts to decide on the new lawsuit.
The lawsuit was filed at the arbitration court of Russia's Bashkortostan region in relation to dividends paid by Bashneft in 2009-2014, when Sistema was its controlling shareholder.
Rosneft said it had "done everything it could" to reach a settlement, while Sistema said it welcomed any effort to try to end the dispute in a way that suited both parties.
Meanwhile, the state-owned Russian Direct Investment Fund (RDIF), which is mediating between the two parties, said it was "making every possible effort to get an amicable settlement in the near future".
(Additional reporting by Maria Kiselyova, Katya Golubkova and Denis Pinchuk; Writing by Andrew Osborn; Editing by Alexander Smith)
By Vladimir Soldatkin and Anastasia Teterevleva