There is “nothing conclusive” in the data that means England “would have to deviate from the roadmap” out of lockdown, Boris Johnson has said.
The government plans to end remaining restrictions on social contact by 21 June, but there is increasing concern about the Indian variant.
The situation, including data from hotspots such as Bolton, was “under close review”, the prime minister said.
Ministers will “let people know in a few days’ time” after data is studied.
Health Secretary Matt Hancock said on Monday that 86 local councils had five or more cases of the variant first discovered in India, which is thought to be more transmissible.
Speaking on a visit to a vaccination centre, Mr Johnson continued to urge people “to be cautious”.
He said the situation with the Indian variant was “under very careful, close review”, saying: “We’re looking at all the data as it comes in from places like Bolton, Blackburn, Bedford, Sefton.”
Mr Johnson said they were trying to understand if the Indian variant was more transmissible and “to what extent our vaccine programme has sufficiently fortified us”.
“We’ve got a few more days of looking at that data,” he said.
The prime minister’s official spokesman said that while the government was not ruling out measures such as local lockdowns at this stage, it was “too early to speculate” on what future measures it may need to take.
Asked if a decision was expected sooner than 14 June on progressing to the final step of England’s roadmap, the spokesman said that in relation to certification and social distancing, ministers “do want to update pubs and businesses, if possible, before 14 June”.
But he added they needed to “allow the experts to do their work” and “couldn’t be more specific on timings”.
The government has already warned its next review of social distancing rules – set to take place by the end of May – may be delayed because of concern over the variant first found in India.
As part of its roadmap out of lockdown, the government’s plan is to end all remaining restrictions on social contact by 21 June – which would mean unlimited numbers of guests at weddings, and venues such as nightclubs being allowed to reopen.
On Monday millions of people were able to enjoy new freedoms – such as drinking indoors in pubs, hugs with loved ones and foreign holidays – for the first time in months, under the latest relaxation of rules across England, Wales and most of Scotland.
Asked about people travelling to “amber list” countries – which are subject to testing and quarantine rules – Mr Johnson said it was “very important people grasp what the amber list is – not somewhere to go on holiday”.
He said travellers should only go to these countries for “pressing family or business reasons”. Those who break their self-isolation period on returning to the UK from these destinations face £10,000 fines, he said.