Miller said this week's annulment of the so-called Kharkiv accords, which gave Ukraine cut-price Russian gas until 2017 in exchange for access to the Crimea's port facilities, means that Kiev should pay the sum total of this discount back.
"The sum of the discount granted in the time that the Kharkiv accords were valid was USD 11.4 billion. That is the sum that the Russian government, the Russian budget did not receive," Miller told Russian television.
"Russia was paying for the Black Sea Fleet in Ukraine... towards prolonging the agreement. That is, Russia was paying an advance. Therefore, the USD 11.4 billion is a debt that Ukraine has accrued to Russia," he said.
Tensions between Moscow and Kiev have been running high since Russia annexed Crimea last month in defiance of the international community after pro-European demonstrators ousted Ukraine's pro-Kremlin leaders.
Gazprom is also seeking immediate payment for all recent gas deliveries to Ukraine, valued at over USD 2.2 billion.
Moscow has repeatedly shown readiness to use gas as a lever in conflicts with Ukraine, which remains dependent on imports from its resource-rich former Soviet master to keep the country running.