Matt Hancock said he didn't "want to speculate" on the possibility of tougher measures being brought in as coronavirus rates continue to rise.
Asked about the prospect of tighter restrictions, the Health Secretary told BBC One's Andrew Marr Show: "I don't want to speculate because the most important message is not whether the government will further strengthen the rules.
"The most important thing is that people stay at home and follow the rules that we have got.
"And that, in terms of the scale of the impact on the cases, that is the most important thing we can do collectively as a society."
Mr Hancock, who gave the interview from his own home via video link, added: "It is hard, it is not easy. But if you can do something from home and you don’t need to go outside of home to do it, then you should.
"People need to not just follow the letter of the rules but follow the spirit as well and play their part."
His comments come after a public health expert said lockdown in the UK should continue for the next 12 weeks - double the length the government has suggested.
Professor Devi Sridhar, chair of public health at Edinburgh University, told Times Radio that, although lockdowns are "crude" and "catastrophic" for the economy and mental health, one is needed given the prevalence of Covid-19 across the UK currently.
But, Prof Sridhar said, a post-lockdown strategy must be put in place to suppress the virus going into the summer.
She said: "With the numbers we’re at, there’s no other choice.
"For me, it's a three-phase strategy – first is right now, it's crude, it's catastrophic for the economy and for people's mental health, but a lockdown.
"Get those numbers down, protect the NHS for the next 12 weeks."
