Around 600 of the 1,600 filling stations around Ireland have run dry, according to an industry representative.
Fuels for Ireland Chief Executive Kevin McPartlan said he expects the number "will grow quite dramatically" if ongoing blockades of fuel depots remain in place.
Asked on RTÉ's The Business how that number may grow, he said: "If everything remains as it is, that is to say that the three facilities remain blockaded, then I don't think we could guarantee fuel at any forecourt by very early next week, Monday morning or Monday perhaps."
Speaking later, Mr McPartlan said if blockades continue at the Whitegate Refinery and the terminals at Foynes and Galway, it is likely that two thirds of petrol stations in Ireland will be out of stock by the end of the day.
Mr McPartlan said that just over one third of the 1,600 petrol stations across the country are currently out of fuel. He urged people not to get petrol.
"I understand that people are anxious about fuel supply," but, he said, "if you don't need fuel at the moment just pause, it's going to be fine in a few days, just give us a chance to recover".
He said Ireland has plenty of fuel but access to the terminals is needed.
"If the gardaí can secure those routes in and out of those terminals, as we hope they will do today, we should be able to start restoring normal service."
Mr McPartlan said it will take a few days once access is granted, or maybe a week, to get every site that has run, or is running dry of fuel, fully restored.
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The CEO said he is "disappointed with the level of response from the State" when he warned about the protests on Good Friday, four days before they started.
Mr McPartlan said that now is not "the time for recriminations" and that the Taoiseach has agreed there will be a "lessons learned exercise when this is all over".
"We will fight about what went wrong then, but for now the focus is just about getting everything restored."
Mr McPartlan said the Government and gardaí are putting all their efforts into fixing the problem, adding, "mistakes were made early on, lets get over those and move on".
Additional reporting PA
