The Cabinet minister said he is “puzzled” by a report suggesting that their universal availability could be axed as they are limited to high-risk settings and for people with symptoms.
But he indicated support for reducing the isolation period from seven days to five, if it can be done safely, in order to reduce staffing pressures on the NHS and businesses.
The Sunday Times reported that Prime Minister Boris Johnson would make the announcement on scaling back tests within weeks, while the NHS Test and Trace system could also be diminished.
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But Mr Zahawi told Sky’s Trevor Phillips on Sunday: “I saw that story this morning, which I was slightly puzzled by because I don’t recognise it at all. This is absolutely not where we are at.
“For January alone we’ve got 425 million lateral flow tests coming in and they will continue to be available for free.
“I don’t really recognise where that story is coming from.”
Asked whether there are plans to stop lateral flow tests being free, he said: “Absolutely not.”
But Liberal Democrat health spokeswoman Daisy Cooper pointed out that vaccines minister Maggie Throup confirmed early in December that “at a later stage” the “free universal provision of LFD (lateral flow device) tests will end”.
Ms Cooper said the “left hand doesn’t know what the right hand is doing” as she warned that scrapping free tests “would plunge millions into a cost of living with Covid crisis”.
The criticism came as the Government seized on suggestions from scientists that the emergence of the seemingly less deadly Omicron strain is a step towards the virus becoming endemic, or regularly occurring, but easier to live with.
Mr Zahawi said the UK Health Security Agency will investigate whether the isolation period can be reduced to help alleviate staffing pressures.
“It would certainly help mitigate some of the pressures on schools, on critical workforce and others,” he told Sky.
“But I would absolutely be driven by advice from the experts, the scientists, on whether we should move to five days from seven days. What you don’t want is to create the wrong outcome by higher levels of infection.”
Mr Zahawi anticipated a “bumpy” two weeks as more school staff end up off work isolating for coronavirus as case rates rise when pupils return.
He told the BBC’s Sunday Morning show that staff absenteeism was at around 8.5% last week but “will increase, no doubt, because now schools are back we’re going to see an increase in infection rates”.
“I have to have contingency plans for 10, 15, 20, 25% absenteeism because Omicron is far more infectious,” he added.
Mr Zahawi’s comments came after the number of people to have died in the UK within 28 days of a positive Covid test passed 150,000.
The country was the seventh to pass the milestone for officially recorded deaths, following the US, Brazil, India, Russia, Mexico and Peru.
Rapid tests were made available to everyone in England, crucially including those without symptoms, in April.
They have been seen as a key way of suppressing the virus and have given confidence to people to safely mix with loved ones, particularly around Christmas.
But the Sunday Times report suggested there are concerns in Whitehall over their cost.
Ms Sturgeon questioned how the move in Westminster would affect funding for the “vital” tests in Scotland, adding: “Hard to imagine much that would be less helpful to trying to ‘live with’ Covid.”
Shadow health secretary Wes Streeting warned that charging for tests would hit families who are already facing a “cost-of-living crisis”.
“Testing is absolutely crucial for keeping infections under control and avoiding the need for further restrictions that impact on our lives, livelihoods, and liberties,” he said.
“It’s penny wise and pound foolish.”