Matt Hancock said it was “too early” to determine whether the lockdown measures in England would end after December 2.
Asked whether the lockdown would simply be “rebadged” after the deadline, he told BBC Radio 4’s Today programme: “You tempt me, but it is too early to say I’m afraid.
“We’ve seen in the last week that there is still a very high number of cases but we do absolutely want to come out of this national lockdown.
“That is our goal, everybody has a part to play in making that happen of course, following the social distancing rules and isolating when you need to, which is the critical thing.”
He said one of the main goals now was to use the mass rapid testing roll-out to find those who are asymptomatic with the virus.