Hospitals should use spare laboratory space to test self-isolating NHS staff in England for coronavirus, Health Secretary Matt Hancock has said.
The government faces growing criticism over a lack of testing for frontline staff who could return to work if found clear of the virus.
On Tuesday, Cabinet Office minister Michael Gove admitted the UK had to go "further, faster" to increase testing.
It came as a 13-year-old boy from south London with coronavirus died.
Ismail Mohamed Abdulwahab, from Brixton in south London, is thought to be the youngest reported victim of the disease in the UK.
His family, who said they were "beyond devastated" by his death, said Ismail had no apparent underlying health conditions and tested positive for Covid-19 on Friday, a day after he was admitted to hospital.
It has also been confirmed that a "healthy" 19-year-old with coronavirus died shortly after arriving at North Middlesex Hospital on 24 March.
The latest daily death toll in the UK rose sharply to 381, taking the overall number of deaths to 1,789, as of 17:00 BST on Monday.
Mr Gove described the rise as "deeply shocking", adding that "now is absolutely not the time for people to imagine there can be any relaxation or slackening" of lockdown measures.
Testing so far has focussed on patients, though NHS England has told hospitals to use up to 15% of their testing capability on staff, if this is possible.
Mr Hancock has now urged hospitals to go further and test as many staff as they can, with health officials saying laboratories have the capacity to take on more tests.
The government has been repeatedly criticised for having said in recent weeks that testing was a priority, but then not implementing it for frontline NHS workers.
Ministers have announced plans to work with the private sector and universities to scale up testing.
But Mr Gove said at the press briefing that the ability to increase testing capacity was being hampered by the availability of the chemicals needed to test patients.
An immediate problem to fix
There is much confusion over the issue of testing and a multitude of figures flying around. That reflects uncertainty at the highest levels of Whitehall on what is really going on.
It's a critical issue for the NHS: Doctors and nurses who are self-isolating need to be tested, so that if they do not have the virus, they can quickly return to work, at a time when staff are badly needed on the frontline.
The government target is to get to 25,000 people being tested each day - a goal which has now been shifted back until late April. An earlier target set at 10,000 should have been hit by now. The daily testing total is still at about 8,000.
Then, there's laboratory capacity, which, according to officials, should allow 12,500 tests to be analysed each day and 15,000 by the end of this week.
So why is that capacity not being used?
That remains a bit of a mystery. If it can be solved then many more NHS staff could be tested. A global shortage of chemical supplies has been blamed by Michael Gove.
But the full answer is probably more complex.
Testing kits are hard to find in some areas. There is likely to be inefficiency in the organisation of testing processes and laboratory analysis.
When the pandemic is over, many questions will be asked about whether the UK did order enough kit and supplies early enough.
Right now, ministers and officials have an immediate problem to fix.
Chris Hopson, the chief executive of NHS Providers, said if existing NHS pathology labs had unlimited swabs and reagent, there would be enough test machine capacity to process around 100,000 tests a day.
But Mr Hopson said a "reagent and swab shortage is currently limiting this to [around] 13,000 a day".
The government hopes to be able to process 15,000 tests for NHS staff in the coming days, according to Communities Secretary Robert Jenrick.
The Chemical Industries Association acknowledged demand was "escalating" but said reagents - used to find out if a reaction occurs - were being manufactured and delivered to the NHS.
And shadow international trade minister Bill Esterson told the BBC: "I asked the chemical industry [on Tuesday] and they said to me their member companies aren't aware of any shortage."
Mr Gove said Prime Minister Boris Johnson and Mr Hancock - who are both self-isolating after testing positive for Covid-19 - were working with companies worldwide to get the materials needed.
Speaking at the government's daily coronavirus briefing, Mr Gove said: "More NHS staff are returning to the front line, and more testing is taking place to help those self-isolating come back, and to protect those working so hard in our hospitals and in social care.
"But while the rate of testing is increasing, we must go further, faster."
A fifth of nurses have been affected, the Royal College of Nursing said, while the British Medical Association said staff began being tested over the weekend, but only in low numbers.
BMA chairman Dr Chaand Nagpaul said: "It's been well over two weeks since the government said it was going to roll out priority testing for healthcare staff.
"But many doctors still have no idea about where or how they can get tested."
Conservative former Health Secretary Jeremy Hunt said it was "very worrying" that the government had not introduced mass testing.
He said it had been the key to finally controlling the outbreak in Wuhan, the Chinese city where the disease first appeared. "It is internationally proven as the most effective way of breaking the chain of transmission," Mr Hunt said.
Professor David Heymann, a former chair of Public Health England, told BBC Radio 4's Today programme the government was implementing community studies to determine hotspots of infections in Britain.
"I happen to know that there are studies being planned by Public Health England and by others around the UK to determine what the actual extent of transmission has been," he said.
In other developments:
- Prince Charles has spoken of the "distressing" effect of isolation following his recovery from coronavirus
- The Edinburgh Festival, due to take place in August, has been cancelled
- The Ministry of Defence said 80 armed forces personnel would be sent to staff ambulances and 999 call centres across Berkshire, Buckinghamshire, Hampshire, Oxfordshire, Sussex and Surrey
- Some of the UK's biggest banks have agreed to scrap dividend payments and hold onto the cash, which may be needed during the coronavirus crisis
- New research suggests a loss of smell or taste may be a sign that you have coronavirus
- A coronavirus app that alerts people if they have recently been in contact with someone testing positive for the virus "could play a critical role" in limiting lockdown
- Pregnant prisoners could be granted temporary release from prison "within days" to protect them and their unborn children from the virus
How have you been affected by the issues relating to coronavirus? Share your experiences by emailing email@example.com.
Please include a contact number if you are willing to speak to a BBC journalist. You can also contact us in the following ways: