"We would find a way not just to reduce our dependency on the United States to zero but to emerge from those sanctions with great benefits for ourselves," said Kremlin economic aide Sergei Glazyev.
He told the RIA Novosti news agency Russia could stop using dollars for international transactions and create its own payment system using its "wonderful trade and economic relations with our partners in the East and South."
Russian firms and banks would also not return loans from American financial institutions, he said.
"An attempt to announce sanctions would end in a crash for the financial system of the United States, which would cause the end of the domination of the United States in the global financial system," he added.
He said that economic sanctions imposed by the European Union would be a "catastrophe" for Europe, saying that Russia could halt gas supplies "which would be beneficial for the Americans" and give the Russian economy a useful "impulse".
Glazyev has long been seen as among the most hawkish of the advisors to President Vladimir Putin but many observers have seen his hand in the apparent radicalisation of policy on Ukraine since the overthrow of president Viktor Yanukovych.
Economists have long mocked his apocalyptic and confrontational vision of global economics but also expressed concern that he appears to have grown in authority in recent months.
A high ranking Kremlin source told RIA Novosti that Glazyev was speaking in the capacity of an "academic" and his personal opinion did not reflect the official Kremlin policy.
Glazyev descrived the new Ukrainian authorities as "illegitimate and Russophobic", saying some members of the government were on lists of "terrorist organisations, they are criminals".
"If the authorities remain criminal then I think the people of Ukraine will get rid of them soon," he added.