Mr Hancock told Sky News' Trevor Phillips On Sunday programme that vaccines had "severed but not broken" the link between a rise in cases and an increase in the number of people being admitted to hospital.
Mr Hancock admitted the emergence of the Indian variant, which has become dominant in the United Kingdom, had made the "calculation" on whether to proceed with unlocking this month "more difficult" as he revealed the latest scientific advice is that the mutation - also known as the Delta variant - is 40% more transmissible than the Kent strain.
The spread of an infectious COVID-19 variant in Britain has cast doubt on whether the country will go through with its plan to fully repeal its pandemic restrictions on June 21.
Two doses of vaccine are needed for strong protection against Covid, particularly the variant first found in India - also known as B.1.617.2 or Delta - that has been causing outbreaks around the UK.
Public Health England said last month that research showed double vaccination was similarly effective against both the Alpha and Delta variants. Hancock said the 40 percent figure came from the government body of scientific advisors, SAGE. One of the four critical tests set by the government for a reopening is that the assessment of the risk from the deadly virus is not fundamentally changed by new VOC.
"We are not saying "No" to June 21 at this point", Matt Hancock said.
The government has indicated that the wearing of face coverings and working from home measures could continue in the long-term, beyond that date.
"The way we are looking at this is step four [of the roadmap] involves the removing of the remaining social restrictions like the rule of six and some of the business closures which are still there".
"And separately we have a piece of work on what the social distancing rules should be after that".
The drive to roll out vaccines to every adult by the end of July is continuing at pace as the Health Secretary announced those aged under 30 will be invited to book for their first dose this week. So far hospitalisations are "broadly flat", with very few hospitalised after receiving both vaccine doses, he added.
Vaccination can help stop the spread of coronavirus as well as protect people from getting sick.
The UK has recorded nearly 128,000 coronavirus deaths, the highest toll in Europe.