"The supplemental agreement provides for amendments to the terms of the contract in terms of price, volume and conditions of supply of natural gas," the heavily indebted Ukrainian company said in a statement, without providing more details.
Gazprom has threatened to cut off gas supplies to Ukraine if Naftogaz fails to pay some of its $3.5 billion debt for imported gas.
Naftogaz said in the statement it paid Gazprom on May 30 $786.3 million for February-March supplies, and hence, "fully paid for the supply of natural gas to Ukraine for the first quarter of 2014 at the price of $268.5 for 1,000 cubic metres".
Russia's energy minister has said Moscow and the European Union have proposed that Kiev pay Gazprom $2 billion by May 30, and another $500 million before June 7, as a precondition for a price discount and further talks.
The fourth round of talks between Ukraine, the European Union and Russia are scheduled for later on Monday.