After Unite, the union representing 2,000 fuel tanker drivers, ruled out the threat of strikes over Easter, the Government last night changed its advice to drivers.
After days of urging motorists to fill up if their tanks dropped below two-thirds full, the Department for Energy and Climate Change said there was no need to queue on petrol forecourts.
"There is no urgency to top up your tank, a strike will not happen over Easter," it said.
But with Unite stressing it retained the right to call industrial action if talks, expected to start next week, break down, No 10 stressed the threat was not yet over.
"It remains vital we take the necessary steps to keep the country safe in case there is a strike," a spokesman said.
The move followed more panic-buying at garages across the country today and the revelation that petrol sales increased by almost 172 per cent yesterday while sales of diesel were up by almost 77 per cent.
Unite and the seven distribution companies involved in the dispute are in contact with Acas but no substantive talks will be held until next week.
Assistant general secretary Diana Holland said: "We will not be calling Easter strike action as we focus on substantive talks through Acas.
"We do still retain the right to call strike action for after Easter, should those talks break down.
"It should be stressed that what we are seeking is reasonable and no more than what is in place elsewhere in the industry.
"This is not a political dispute. It is an industrial dispute and the Government's recent rhetoric will not help us achieve a negotiated settlement."
An Acas spokesman said: "We are pleased that Unite have confirmed they are ready to start substantive talks as soon as possible.
"We are meeting all of the employers involved in the dispute on Monday to complete our exploratory talks with them.
"We hope that more formal talks involving both Unite and the employers will start as soon as possible after Monday."
The Prime Minister said: "It is now clear there will not be a strike before Easter and I'm sure the whole country will welcome that news.
"It is vitally important the trade union in question enters these talks on Monday constructively. The most constructive thing they could do would be to call off the strike entirely.
"That would ease pressure in the system still further. The Government will continue with its contingency plans."
Senior Conservative MP Bernard Jenkin criticised the way the ministers had provoked panic-buying after a week of difficult headlines for the Government.
"My feeling is this was to try to take people's minds off donors, the Budget and pasties - and the Government added to the heat on this," he told the BBC's Sunday Politics East programme.
"But really there should not have been any move to encourage people to buy more than they normally buy without consulting the industry first. I think that was the mistake."
A spokeswoman for BP said demand had eased following the new Government advice.
"It has eased, certainly from yesterday. There is less demand on forecourts," she said.
"However there is still above normal demand. We are making deliveries as quickly as possible to sites and are working 24/7 to get fuel to sites that are running or have run out.
"We have got very few sites that have run out completely - they might have run out of diesel or of petrol - but we are doing our best to replenish sites as quickly as possible.
"We urge people to heed the Government's latest advice."
A spokeswoman for Morrisons, which owns and operates 301 petrol stations, said: "Our supply chain is working at full capacity to ensure sites are replenished and we can continue to keep up with customer demand.
"We have experienced only a handful of temporary stock-outs at sites which were quickly resolved."