Boris Johnson's sister, Rachel, says Dominic Cummings should admit he 'messed up'.
Ms Johnson said the country would be able to move on from outrage over the behaviour of her brother's top aide if he apologised.
It comes amid a growing revolt in Boris Johnson's party, with at least 30 Tory MPs having now publicly called for Mr Cummings to be sacked or to resign.
And a YouGov survey for The Times showed the Conservative lead over Labour dropped by nine points during the Cummings saga, as support for the Government fell four points to 44% with Labour rising five points in the week to Tuesday, to 38%.
Senior ministers have expressed public support for the defiant adviser but there are reports a number of Cabinet members have privately called for him to be ousted from No 10.
Ms Johnson told ITV's Good Morning Britain: "He's (Mr Cummings) been the architect of so many of the winning messages for the Vote Leave campaign, for the Tory party in 2019, and therefore his approach to this is now being seen to have been in some way hypocritical."
"You know, he's been a rule-maker but not a rule-taker, and it's essentially very problematic."
She added: "Obviously everything is bigger than Dominic Cummings, the pandemic is bigger than Dominic Cummings, and as my brother says, nobody would have his unconditional support.
"I think that if I had been Cummings, I'd have admitted I'd messed up and I'd have got on the front foot and said, 'I apologise for all of those who followed my messages, I took bad decisions at the time and I understand how angry it's made a whole country feel, and please let's move on because we have bigger fish to fry'."
The Prime Minister will be quizzed at a Commons committee meeting on the decision of Mr Cummings to drive from London to Durham during the shutdown.
