The fuel situation in the UK is starting to improve, PM Boris Johnson has said - as he urged motorists to fill up their cars in the "normal way".
He said the situation at fuel stations was "stabilising" and people should be "confident" to go about their business, after days of queues and pump closures.
Labour said the government had let the country "crash from crisis to crisis".
Defence Secretary Ben Wallace has approved a request for 150 military tanker drivers to help deliver fuel.
Training the drivers to use civilian fuel company tankers is expected to take place over the next three days, so the first deliveries could take place by the end of the week.
With some drivers continuing to face difficulties in refuelling, there have been calls for key workers, such as health and social care staff, to receive priority at the pumps.
As the prime minister made his first public comments on the fuel supply problems, he was asked if he supported prioritising workers such as NHS staff, responding that "with things stabilising - the best thing is - we stabilise in the normal way".
Mr Johnson said he sympathised with people who had been unable to get fuel over recent days, calling it "frustrating and infuriating".
"What we're hearing from the industry is the situation at forecourts is stabilising," he said.
"I would just urge everyone to go about their business in the normal way and fill up when you need it."
A government source confirmed reports that 16% of all petrol stations were now fully supplied with fuel, compared to 10% at the weekend during some of the worst of the fuel rush.
The source said that 40% of petrol stations being fully supplied was a more normal figure before the rush on fuel.
The Petrol Retailers Association (PRA) said there were "early signs" the pressure was starting to ease at the pumps.
The PRA, which represents nearly 5,500 of the UK's 8,000 stations, said around 37% of its sites had run out of fuel - compared with two-thirds being without on Sunday.
PRA executive director Gordon Balmer said: "With regular restocks taking place, this percentage [of petrol stations with fuel] is likely to improve further over the next 24 hours.
"Fuel stocks remain normal at refineries and terminals, although deliveries have been reduced due to the shortage of HGV drivers."
The government has said people needlessly buying fuel has led to queues at many forecourts, with fuel running out in some places.
Earlier on Tuesday, Transport Secretary Grant Shapps said there were "tentative signs" the situation was starting to stabilise but added that "won't be reflected in the queues as yet".
The UK is estimated to be short of more than 100,000 lorry drivers - causing problems for a range of industries, including food suppliers and supermarkets, in recent months.
The prime minister said panic buying of petrol followed a "slightly misleading" account of the shortages of lorry drivers which caused an "understandable surge in public demand".
He said: "The actual number of lorry drivers that we're short in that particular sector isn't very big. But generally there is a shortage in that profession around the world."
Mr Johnson said the government was taking action to ensure there were enough deliveries in all industries during the run-up to Christmas.
"What we want to do is to make sure we have the preparations necessary to get through to Christmas and beyond, not just in the supply of our petrol stations but all parts of our supply chain," he said.
Labour leader Sir Keir Starmer said he had talked to hauliers earlier in the day and was told that the government was in denial over the problems.
"These were their words, they said, 'it's a government that is denying there's a problem, then blaming somebody else, and then coming up with a half-baked plan'."
He said the government should "give priority to key workers" to get petrol, and "issue enough visas" to deal with the shortage of lorry drivers.
"The government has reduced the country to chaos as we crash from crisis to crisis. And the government is not gripping this," he said.
Doctors, nurses, and unions for teachers, prison and care staff are among those who have called for essential workers to be given priority for fuel.
Some patients relying on vital services delivered in their homes have complained of missed appointments because of the fuel crisis.
Sarah Jane Barnes, from Berkshire, told the BBC that her elderly mother had missed two out of three dialysis appointments because health workers were unable to get enough fuel to reach her.
Rosemary Botting, who runs Karosel Care and Domestic Services in West Sussex, said one of her carers was half an hour late to her first call because of traffic caused by queues at petrol stations.
She said that meant her carer's first patient was unable to get out of bed until she arrived, while it also had a knock-on effect on her other patients.
Dr Jane Townson, chief executive of UK Homecare Association, warned that some people who depend on carers for tasks like taking pain medication could die if they are left without help.
Unison urged ministers to "designate fuel stations for the sole use of key workers" while the NASUWT union called for teachers to be prioritised to safeguard children's education.
Roger Grosvenor, of the East of England Co-op petrol stations, told the BBC the group would create a daily priority hour for emergency workers if fuel supply problems had not eased by Thursday.
Meanwhile, footage emerged on social media of confrontations taking place on petrol forecourts, including a man threatening a motorist with what appears to be a knife in south-east London.
Up to 150 military tanker drivers will prepare to deliver to forecourts which have run dry because of panic buying.
Business Secretary Kwasi Kwarteng said the government's move to place the Army on stand-by was a "sensible, precautionary step".
The government has also authorised an extension to special driver licences that allow drivers to transport goods such as fuel.
ADR licences due to expire between 27 September and 31 December will have their validity extended until 31 January 2022, without refresher training or exams.