Matt Hancock has said he did not watch all of Dominic Cummings' testimony to MPs because he was "dealing with getting the vaccination rollout going...and saving lives".
Mr Cummings, the prime minister's former chief adviser, had earlier repeatedly attacked the health secretary during a seven-hour-long committee hearing.
In response, Mr Hancock said: "I haven't seen his performance today in full.
"Instead I've been dealing with getting the vaccination rollout going, especially to over 30s, and saving lives.
"I'll be giving a statement in the House of Commons tomorrow (Thursday) and I'll have more to say then."
Mr Cummings had told the joint science and technology and health select committee: "I think the secretary of state for health should have been fired for at least 15, 20 things, including lying to everybody on multiple occasions in meeting after meeting in the cabinet room and publicly.
"There's no doubt at all that many senior people performed far, far disastrously below the standards which the country has a right to expect. I think the secretary of state for health is certainly one of those people."
Mr Cummings said he had encouraged Boris Johnson to sack Mr Hancock, and claimed the cabinet secretary Sir Mark Sedwill - the country's top civil servant - recommended the same course of action.
Mr Cummings said it took too long to get the test and trace programme set up, and that in April, the "system was too distracted by the Hancock pledge" to reach 100,000 tests a day, which the former adviser described as "stupid".
"I said: 'If we don't fire the secretary of state and we don't get testing into someone's hands, we are going to kill lots of people'."
Mr Cummings said Mr Johnson "came close to removing" Mr Hancock in April last year, "but just fundamentally wouldn't do it".
Mr Hancock also used chief medical officer Professor Chris Whitty and chief scientific adviser Sir Patrick Vallance as "shields" to blame for his failures, Mr Cummings claimed.
Earlier on Wednesday evening a spokesperson for Mr Hancock said he had "worked incredibly hard in unprecedented circumstances to protect the NHS and save lives".
The spokesperson added: "We absolutely reject Mr Cummings' claims about the health secretary."
Downing Street did not deny that the prime minister considered sacking the health secretary in April last year but insisted Mr Johnson has confidence in him now.