Culture Secretary Oliver Dowden said testing passengers at airports is not a “silver bullet” allowing restrictions to be eased.
He made the comments as the boss of Heathrow Airport declared the UK “needs a passenger testing regime and fast”.
Chief executive John Holland-Kaye claimed travellers are being forced to play “quarantine roulette”.
The UK reimposed the self-isolation requirement for people arriving from Spain on Sunday, making the announcement just five hours before the change in policy came into force.
Mr Dowden told BBC Radio 4’s Today programme: “We are not at the point where there is a viable alternative to the 14-day quarantine.
“There is a real risk here – the virus is spreading around the world, it’s rising rapidly around the world.
“We need to ensure that the measures we’ve taken in the UK – which have been very difficult – to keep this virus under control, do not go to waste because we allow cases to come in from elsewhere.”
Appearing on BBC Breakfast, he said coronavirus can “incubate over a period of time”, adding: “There’s not a silver bullet of just testing immediately at the border.”
Preliminary modelling from the London School of Hygiene and Tropical Medicine suggested 94% of cases would be detected if the quarantine period was cut to eight days and passengers tested negative on the seventh.
Shorter quarantine periods “can prevent a substantial amount of transmission”, the research indicated.
Some 88% of cases would be identified if travellers self-isolate for six days and test negative on the fifth day, according to the study.
Mr Holland-Kaye told the PA news agency that the airport is “ready to go in two weeks” if the Government allows tests to be used to ease restrictions.
He said: “We’ve started to mobilise on that so we can be ready as fast as possible.
“The speed really depends on the Government and them putting the legislation in place to allow people to come out of quarantine early if they have passed two tests, and deciding whether the second test has to be after five days or eight days or some other time.”
Heathrow is working with travel assistance company Collinson and ground-handling firm Swissport to develop an airport testing regime.
Passengers would be charged around £140 per test.
Public Health England and the Department of Health and Social Care have met with Collinson to discuss its proposal.
Mr Holland-Kaye added: “Our European competitors are racing ahead with passenger testing. If the UK doesn’t act soon global Britain will be nothing more than a campaign slogan.”
Around 70% of Heathrow’s pre-pandemic demand was on routes not included on the Department for Transport’s quarantine exemption list.
The airport’s passenger numbers were down 96% year on year between April and June.
It made a pre-tax loss of £1.1 billion in the first six months of 2020, down from a £7 million profit in the same period a year ago.
This came on revenue of £712 million, around half of 2019’s levels.
Tour operator Tui has extended the suspension of holidays to the Balearic Islands and Canary Islands for UK customers until August 4.
Holidays to mainland Spain remain cancelled until August 10.
Tui will increase flights to Greece and Turkey this weekend to enable more affected customers to switch destinations.