Matt Hancock has warned that face masks and working from home guidance could stay in place after the June 21 unlocking, in a bid to allow the majority of other restrictions to be lifted.
The Health Secretary said while the data did not demonstrate "we are definitively off track" with plans to move to the final stage of the unlocking process later this month, he cautioned that it was too early to tell.
And asked specifically about some measures such as mask-wearing and working from home, he said further decisions would be made in the coming weeks.
The Times previously reported that ministers wanted to "prioritise" the ending of social-distancing measures such as the rule of six and the one-metre plus rule, which would help the hospitality industry get back on its feet.
Following the rise in cases and Indian variant surge ministers could decide to keep some less restrictive measures in place.
Mr Hancock told a press conference at the Jenner Institute in Oxford: "There is nothing in the data to suggest we are definitively off track but it is too early to make the decision about June 21, step four in the road map.
"We'll make that decision based on more data in the next week to 10 days, ahead of June 14, as we've set out."
His comments come after Boris Johnson insisted there is "nothing in the data at the moment" to prevent ending Covid-19 restrictions, as the proportion of deaths involving the virus fell to the lowest level in eight months.
But the Prime Minister also warned there is a need for caution, saying there is "no question" of an increase in infection rates.
Latest figures from the Office for National Statistics (ONS) show 9,860 deaths from all causes registered in the week ending May 21, and of these, 1.1% (107 deaths) had "novel coronavirus" mentioned on the death certificate.
The last time the proportion was so low was in the week ending September 11, when the virus accounted for 1.0% of deaths, according to PA news agency analysis.
It was also confirmed on Wednesday that 75% of UK adults across the UK had now had their first coronavirus jab, and 50% of adults in England had received both doses.
Debate is continuing over whether the final stages of unlocking restrictions in England can go ahead on June 21, due to concerns over the spread of the coronavirus variant first identified in India.
Mr Johnson warned: "We've got to be so cautious because there's no question, the ONS data of infection rates is showing an increase.
"We always knew that was going to happen."
But he added: "What we need to work out is to what extent the vaccination programme has protected enough of us, particularly the elderly and vulnerable, against a new surge.
"And there, I'm afraid, the data is just still ambiguous."
