The offer of a 6.3 percent stake in Detsky Mir was priced early on Tuesday, with Sistema selling 5 percent and the Russia-China Investment Fund selling a 1.3 percent stake.
A few hours later, a Russian regional court froze Sistema's stake in Detsky Mir as part of a broader injunction covering $1.7 billion (£1.2 billion) of its assets.
The offering cannot be completed "due to investor concerns triggered by hostile actions initiated by Rosneft and Bashneft", Sistema said in a statement.
The Russia-China Investment Fund said it would also not proceed with the transaction.
"The majority of participants in the offering are leading international investors. The claims and actions of Rosneft and Bashneft have thus put obvious obstacles to the inflow of new foreign investments into the Russian economy," Sistema said.
Rosneft argued Sistema could first pay Rosneft and offer Detsky Mir shares for sale afterwards.
"What have we to do with it ? They can sell these shares after they have paid us ... Nobody asked them to meddle in this senseless circus with us," Rosneft spokesman Mikhail Leontyev said.
Rosneft, which wants Sistema to pay around $5 billion in damages after alleging that its subsidiary oil producer Bashneft was stripped of assets, including dividends, under Sistema's previous ownership, is not seeking control of Sistema's assets, Leontyev said earlier on Wednesday.
The asset freeze, the second to have been ordered in the legal wrangle with Rosneft, caused Sistema's shares to fall by up to 9 percent on Wednesday.
They recovered a little later, but Sistema - which holds the assets of Russian businessman Vladimir Yevtushenkov - has lost a quarter of its market value since the legal battle erupted in early May.
In June, the same court froze assets worth more than $3 billion under a lawsuit filed by Rosneft.
"This is an injunction," Leontyev said of the latest asset freeze on Wednesday. "We don't need the assets, we need the funds ... This is in case Sistema fails or refuses to pay in cash."
The dispute centres on mid-sized oil company Bashneft and pits powerful Rosneft chief executive Igor Sechin, a close ally of President Vladimir Putin, against Yevtushenkov, a billionaire who some media reports suggest is close to Prime Minister Dmitry Medvedev.
The way the battle is being fought - via lawsuits and counter lawsuits - and the high value of the assets involved, has rekindled concerns about Russia's investment climate and raised questions about the Kremlin's oversight of business.
Yevtushenkov was placed under house arrest in 2014 over alleged money laundering before the state renationalised Bashneft, saying its privatisation had been illegal, while dropping all charges against him.
Rosneft then bought a controlling stake in Bashneft from the government in 2016. It later 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 Rosneft's first lawsuit in the case.
Rosneft filed a second $2.2 billion lawsuit earlier this month, and Sistema then counter-sued Rosneft for around $5.6 billion.
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 both companies have accused 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 declined to comment on the legal battle on Wednesday.
($1 = 58.7899 roubles)
(Additional reporting by Dmitry Solovyov, Denis Pinchuk, Katya Golubkova and Oksana Kobzeva; Writing by Andrew Osborn and Maria Kiselyova; Editing by Greg Mahlich)
By Maria Kiselyova and Vladimir Soldatkin