"If the Ukrainian pipeline does not receive the required gas volumes, the pressure in the pipes is going to fall," he said, quoted by AFP news agency.
"As result, there will be interruptions quite automatically, independent of people. The system could even have to shut down so that the pressure comes back."
On Friday, Ukraine's state gas company, Naftogaz, denied illegally siphoning Russian gas, saying it was diverting gas from its own reserves to try to maintain export supplies.
Russia meanwhile has said it increased the volume of gas bound for the EU as it cut supplies to Ukraine.
Consumers 'not hit'
The head of Romania's gas pipeline operator Transgaz said gas supplies had dropped by 30% on Friday.
The deputy chairman of Gazprom, Alexander Medvedev, speaks to the BBC
The head of Bulgaria's state gas concern told Reuters news agency Bulgaria's supply was also falling and that transit to Turkey, Greece and Macedonia was affected.
Officials in both countries said consumers had not so far been affected.
On Friday, Poland reportedly recorded a drop of 6%, and Hungary a drop of almost a quarter.
In his first foreign interview since the gas was cut off to Ukraine, Gazprom's Alexander Medvedev dismissed the suggestion his company was deliberately picking a fight with Kiev.
Instead he said Gazprom was ready to end the dispute immediately - but there was no-one to negotiate with.
Mr Medvedev said Gazprom had gone out of its way to ensure supplies of gas to Europe were maintained.
He said the problem was not with Russia, but Ukraine, adding "that's why we believe it's necessary to develop, as soon as possible, alternative transit routes".
The alternatives are two new pipelines Russia is planning to build that will by-pass Ukraine on their way to Western Europe.
The Nord Stream gas pipeline would run under the Baltic Sea from Russia to Germany, and the South Stream link would pass under the Black Sea.
The BBC's Rupert Wingfield-Hayes in Moscow says this latest dispute is expected to give those Russian plans a significant boost.
Pipes across Ukraine carry about a fifth of the EU's gas needs. A similar row between Gazprom and Ukraine at the beginning of 2006 led to gas shortages in several EU countries.
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