Italy is the latest in a long line of European countries to claim increased Russian gas supply restrictions.
After facing deficits for two days, Eni said it would only receive half of the 63 million cubic metres per day it had sought from Gazprom on Friday.
Germany has accused Gazprom of aiming to raise energy costs by drastically cutting supply.
Repairs to the Nord Stream pipeline, according to Gazprom, are to blame.
Russia provides 40% of the natural gas to the European Union. It also provides 27 percent of the EU's imported oil, for which the EU pays Russia roughly €400 billion ($430 billion; £341 billion) every year.
In reaction to Vladimir Putin's threats, the EU has taken steps to wean itself from Russian fossil fuels. By the end of 2022, most oil imports will be banned due to the invasion of Ukraine.
It has pledged to cut Russian gas imports by two-thirds within a year, but further restrictions, such as an outright ban, have been difficult to agree on.
Member states have been asked to store gas during the hotter summer months in anticipation of increased demand for fuel in the winter, but Russia's recent supply cuts have raised fears that the continent may struggle to build up adequate storage.
If Russia continues to cut supply, two government sources told Reuters that Italy might announce a "state of alert" on gas next week.
A move like this would prompt a slew of consumption-cutting measures, including rationing. On Friday, Slovakia reported getting less than half of the typical levels through the Nord Stream 1 gas pipeline, which runs from Russia to Germany over the Baltic Sea.
Meanwhile, France said that it has not received Russian gas through Germany since June 15, but that it is obtaining supply from other sources.
Germany has accused Gazprom of aiming to raise energy costs by drastically cutting supply, but the energy company claims the delay is due to the delayed return of equipment repaired in Canada by Siemens Energy.
Large drops in Russian gas supplies have also been observed in Austria. The Kremlin has stated that this was not planned.
Russian gas exports to Poland, Bulgaria, Finland, Denmark, and the Netherlands have already been halted.