"Ukraine has paid the first instalment for gas supplies. Today USD 786 million entered Gazprom's account," Miller was quoted as saying in a company statement.
"We welcome Ukraine starting to pay back its debt and postpone the pre-payment regime until June 9.
"The introduction of the pre-payment regime will depend on the full repayment of the debt for gas supplied up to April 1 in the amount of USD 2.237 billion, part of which was paid today, and on the progress in payments for April and May supplies," Miller was quoted as telling journalists in the statement.
Ukraine and Russia are due to hold crunch talks later in the day in Brussels on their long-running dispute over the price of gas.