There is "no shortage of fuel" and people should be "sensible" and fill up only when they need to, Transport Secretary Grant Shapps has said.
It comes as there are long queues and closed pumps at some filling stations.
Mr Shapps blamed the Road Haulage Association for triggering a "rush on petrol stations".
He said he was introducing a "big package" of measures, including temporary visas for lorry drivers, to help the situation.
The transport secretary said there was "plenty of fuel" and that he had checked with the six refineries and 47 storage centres in the country.
But the Petrol Retailers Association said that "between 50% and 90%" of its members' forecourts are dry.
Mr Shapps told the BBC's Andrew Marr said that a shortage of heavy goods vehicle (HGV) drivers was "not anything new" but said "irresponsible briefing" to the press following a meeting with road haulage groups had sparked a reaction from people.
The Mail on Sunday reported that someone from the Road Haulage Association had selectively leaked comments about HGV driver shortages at fuel firms.
But spokesman Rod McKenzie told BBC Radio 4's Broadcasting House that it was "absolute nonsense" and said he had not been at the meeting.
A shortage of lorry drivers has caused problems for a range of industries in recent months, from supermarkets to fast food chains.
In recent days, some fuel deliveries have been affected, leading to lengthy queues at petrol stations - with reports of dozens of cars queuing in London by 07:00 BST on Sunday morning.
Supermarket Sainsbury's said it was experiencing "very high demand for fuel", while Morrisons said it was a "rapidly moving situation" and it was working hard to keep its pumps open.
Asda said it had put a £30 limit on fuel transactions and said that it had good levels of fuel supply.
Brian Madderson, chairman of the Petrol Retailers Association told BBC Radio 4's The World This Weekend that the forecourts which were not dry were "partly dry and running out soon".
"That is something which the government obviously are loathe to recognise," he said. "There is plenty of fuel in this country but it is in the wrong place for the motorist."
Freight industry group Logistics UK estimates that the UK needs about 90,000 HGV drivers - with existing shortages made worse by the pandemic, tax changes, Brexit, an ageing workforce, and low wages and poor working conditions.
Labour leader Sir Keir Starmer said the situation showed a "complete lack of planning" from the government.
He said the situation had been known about for years and said "we knew in particular that when we exited the EU there would be a need for a back-up plan to deal with the situation."
He said Prime Minister Boris Johnson needed to say what he was going to do about the situation on Sunday.
Asked if he would bring in 100,000 foreign drivers, Sir Keir said: "We have to issue enough visas to cover the number of drivers that we need."
Under plans to limit supply disruption in the run up to Christmas up to 5,000 lorry drivers and 5,500 poultry workers could receive UK visas, the government announced on Saturday.
Logistics UK welcomed the policy calling it "a huge step forward in solving the disruption to supply chains".
But the British Chambers of Commerce said the measures were the equivalent of "throwing a thimble of water on a bonfire", while the Road Haulage Association said the announcement "barely scratches the surface".
Mr Shapps said the Covid pandemic had created a problem by preventing tests for new HGV drivers and Ministry of Defence examiners were being drafted in to help increase testing capacity.
He said he did not want to "undercut" British workers by bringing in foreign workers but could not "stand by and watch while queues are forming".
Mr Shapps said the government did not want to be reliant on overseas labour in the long term but said he had acted to reassure people in the short term.
"I'm doing some things we wouldn't necessarily have wanted to do because we believe in fixing this market for the long term so the drivers are paid better, and we welcome that - we think it is a good idea for drivers to be paid more and for conditions to be better," he said.
While 5,000 temporary visas are being assigned for lorry drivers this is for supplying the food industry as well as fuel tankers.
Mr Shapps said there was not a "dramatic shortage in drivers" for the fuel industry with only "one, two, three hundred drivers" needed for distribution to petrol stations.
One of those who struggled to refill their car was Adrienne Kenny, from Cambridge, who needed to drive to Leeds for work on Monday.
She said she had tried three petrol stations on Saturday but "couldn't get diesel anywhere" before trying another six without success on Sunday, leading her to postpone her meeting.
Recruitment for additional short-term HGV drivers and poultry workers will begin in October, with the visas valid until Christmas Eve.
Other measures include sending nearly one million letters to drivers who hold an HGV licence, seeking to encourage them back into the industry.
Poultry workers have also been included in the temporary visa scheme and turkey farmer Kate Martin has warned supermarkets could run out of birds before Christmas.
She said there were fewer turkeys being produced because because the big processors "know they will not get them processed".
"Come Christmas, if you leave ordering your turkey from your local farm supplier, you are going to be out of luck," she added.
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