Coronavirus tests are to be 'prioritised' as Matt Hancock admitted testing chaos would go on for weeks.
The Health Secretary said acute care "is and always has been" the priority for tests, and that social care would be next.
He said a new list of priorities would be published, but did not say when.
Mr Hancock said prioritisation was "a choice that we must make".
But Mr Hancock was bombarded with questions from MPs about people with Covid-19 symptoms who are struggling to access walk-in tests, being sent to far off test centres across the country and being told there are no at-home tests available.
In one baffling anecdote, Twickenham MP Munira Wilson said her constituents couldn't get a test when using their own postcode, but if they put in an Aberdeen postcode they could.
Mr Hancock did not explain the reason for the error - but urged the public not to "game the system."
While he admitted there were "operational challenges" which the government was "working hard to fix" - he continued to blame the public for the chaos.
He said: "We've seen a sharp rise in people coming forward for a test, including those who are not eligible.
"And throughout this pandemic we have prioritised testing according to need."
He added: "I do not shirk from decisions about prioritisation. They're not always comfortable, but they are important.
"The top priority is and always has been acute clinical care. The next priority is social care, where we're now sending over 100,000 tests a day because we've all seen the risks this virus poses in care homes.
"We'll set out in full an updated prioritisation and I do not rule out further steps to make sure our tests are used according to those priorities."
Jeremy Hunt, who chairs the Health Select Committee noted Mr Hancock had last week said issues with the testing system would take "a couple of weeks" to resolve - and asked him whether he was confident they would be solved next week as promised.
Mr Hancock replied: "We will be able to solve this problem in a matter of weeks."
A No10 spokesman could only promise more capacity “in the coming weeks” when a new lab opens in Leicestershire, processing 50,000 tests a day.
Asked if it would be this month or next month, he replied: “As I say, it’s in the coming weeks”.
Asked if there was any hope at all that the situation will improve before that lab opens, he replied: “We’ll continue to target our capacity where we need to do so.
“We will open new labs, we’ve increased the number of testing sites to 500, we’ve announced £500m to pilot new tests to further boost capacity.
“We will continue to work to new capacity and continue to make capacity available to those who need them.”
Despite people across Manchester, Birmingham and other areas reporting they couldn’t get tests, a No10 spokesman claimed: “It’s wrong to say that testing is not available in these areas.” He said slots are regularly re-opened.
The Cabinet discussed testing but a No10 spokesman would not give any detail on what was said.
He said: “Testing was discussed.
“And we’ve been clear that we are committed to working to increase capacity, which is why we recently announced a new lab in Leicestershire which will process around 50,000 tests a day in the coming weeks.”
There is also a new lab in Newport and the number of testing sites has risen to 500, he said.
He added: “We’ve established one of the world’s largest testing programmes from scratch and continue to test over a million people a week.”
Mr Hancock said an updated prioritisation list would be published setting out who will be at the front of the queue for tests.
"We have seen a sharp rise in people coming forward for a test, including those who are not eligible," Mr Hancock said.
"Throughout this pandemic, we have prioritised testing according to need. Over the summer, when demand was low, we were able to meet all requirements for testing, whether priorities or not.
"But as demand has risen, so we are having to prioritise once again and I do not shirk from decisions about prioritisation. They are not always comfortable, but they are important."
