Health Secretary Matt Hancock said increasing numbers of people in England were seeking tests when they didn’t have any Covid-19 symptoms.
He said this “inappropriate” use of the system was making it harder for people who needed tests to get one.
It comes after the boss of England’s testing system apologised to people who were struggling to get tests.
UK labs have reached capacity, meaning some people are struggling to book tests.
Mr Hancock gave the example of one school who sent a whole year group for tests, which is “not appropriate”, he added.
Mr Hancock also described how some people who were going on holiday had sought to get tests.
The free tests are available to people with symptoms of coronavirus – a fever, new and continuous cough or a loss or change in sense of taste or smell.
‘Increase in demand’
Mr Hancock denied the testing system was failing, pointing out the UK had the biggest testing system per head of population of all major European countries.
“Right now, we have the highest capacity for testing that we’ve ever had – increased compared to last week.
“And that testing means that we can find these cases, and therefore help keep the virus under control with the contact tracing system as well.
“However, in the last couple of weeks we have seen an increase in demand, including an increase in demand for people who are not eligible for tests, and people who don’t have symptoms,” Mr Hancock said.
“We have seen an increase of about 25% of people who are coming forward that don’t have symptoms and aren’t eligible. They don’t have a reason for it.
“I’ve even heard stories of people saying, ‘I’m going on holiday next week, therefore I’m going to get a test’. No – that is not what the testing system is there for.
“We’ve got to be firmer, I’m afraid, with the rules around eligibility for testing.”
The BBC has asked the Department of Health and Social Care how the 25% figure has been calculated, but is still waiting for a response.
Labour’s shadow health secretary Jonathan Ashworth said: “It beggars belief that after weeks of encouraging people to have a test if feeling unwell, ministers are seeking to blame people for simply doing what they were advised.
“With children returning to school and thousands returning to the office, it’s obvious extra testing capacity would be needed.
“The fact ministers failed to plan is yet more staggering incompetence.”
On Tuesday, the director of testing in England, Sarah-Jane Marsh said she offered her “heartfelt” apologies to people who could not get a test.
A new lab is due to open in Loughborough in about a fortnight, which will increase testing capacity by about a fifth.