Matt Hancock has formally denied the claim from Dominic Cummings that he incorrectly promised people discharged from hospitals to care homes were being tested for Covid at the start of the pandemic, saying: “No, I did not.”

The rejection, after lengthy questioning on BBC One’s The Andrew Marr Show, follows the health secretary’s previous refusal to deny explicitly the claim in the Commons and at a Downing Street press conference, a day after Cummings’ explosive claims to MPs.

But in an indication of Hancock’s likely approach when he is questioned by the same parliamentary committee on Thursday, he argued that Cummings had not in fact accused him of wrongly claiming tests were already being done in March last year – only that he said they would happen when testing capacity was available.

Questioned as part of a joint inquiry by the Commons science and health committees on 26 May, Cummings said Hancock should have been fired for “at least 15 to 20 things – including lying to everybody on multiple occasions”.

Asked for specifics, Boris Johnson’s former chief aide said: “We were told categorically in March that people would be tested before they went back to homes, we only subsequently found out that that hadn’t happened.”

Playing the clip to Hancock, Marr asked whether he had been completely honest and transparent. Hancock replied: “Yes, of course I have – internally, in private and in public.” He added: “The allegations you refer to are completely wrong.”

Asked about the specific claim that he had promised incorrectly in March that people were being tested for Covid before they were moved from hospitals to care homes, Hancock initially evaded the question.

“The situation with respect to care homes is that we brought in the policy of wanting to test everybody who went in to a care home as soon as we had those tests available,” he said.

“But at the time we didn’t have the testing capacity, and I built that testing capacity, put in place the 100,000 [daily tests] target. And we got the tests, and then we could implement the policy.”

Pressed on whether he had said people were being tested when they were not, Hancock said: “Throughout, some were tested where there were tests available. But there were not enough tests available to test everybody, and the clinical advice at the time was that hospital is a dangerous place for people, who might end up getting Covid after they’ve taken the test but before the result comes through.”

Asked for a “yes or no answer” about whether he had made the false claim on testing, he finally replied: “No, I did not.”

But questioned on whether this meant Cummings was lying, Hancock appeared to argue that the former No 10 aide had not been accusing him of what was assumed at the time.

He said: “No, because in what he just said, he said that people ‘would be’, and the truth is, of course that was the policy: to get those tests available. But I had to build this testing capacity. It didn’t exist.”