Theresa May has said Dominic Cummings' trip to Durham was not abiding by the "spirit" of the lockdown guidance and she could "well understand the anger" it caused.
The former prime minister said the actions of Boris Johnson's chief adviser revealed a mismatch between what the Government had been telling the public to do and the intricacies of the coronavirus legislation.
Mr Cummings said he drove from London to his family's farm in Durham after his wife fell ill, and he feared there would be no one to look after their four-year-old child.
In a statement to her constituents in Maidenhead, Berkshire, Mrs May wrote: “In these circumstances I do not feel that Mr Cummings followed the spirit of the guidance.
“I can well understand the anger of those who have been abiding by the spirit of the guidance given by the Government and expect others to do so.
“What this matter has shown is that there was a discrepancy between the simple messages given by the Government and the details of the legislation passed by Parliament."
However, Mrs May said it was important not to let the incident take focus away from tackling the pandemic.
She added: “One of my biggest concerns has been that the ongoing focus on Mr Cummings has been detracting from the most important task, which is dealing with Coronavirus and starting the process of recovery and easing lockdown.”
More than 30 Conservative MPs have called for Mr Cummings to resign.
Durham Police concluded that he did not commit an offence by driving from London to Durham, but he may have committed a minor breach of lockdown rules by making a separate trip to Barnard Castle while he was in Durham.