Prime minister Boris Johnson said: "I know the toll that lockdown has taken on families and friends who have been unable to see each other".
In an email to her Portsmouth North constituents, seen by The Guardian, she said: "Other families have been faced with the same situation Mr Cummings and chosen to stay put".
But one minister has quit in protest and dozens of Tory MPs have publicly called for Mr Cummings to leave his post.
Johnson hinted on Wednesday during the Liaison Committee that pubs and restaurants could reopen as the government are working "as fast as they can" to reopen the hospitality sector.
In an indication of the difficulties Mr Cummings' actions are causing at the top of Government, ministers were forced to deny that a review was being launched into fines issued to other people travelling with their families.
Ahead of the PM's announcement, a Downing Street spokesperson said he had consulted with the leaders of the devolved nations. But the force said "there is no intention to take retrospective action". The reason you're dodging this is because, the reason why you are not giving people a direct answer, is because you are trying to protect Dominic Cummings.
Mr Johnson said "closing schools has deprived children of their education".
In a letter to constituents first reported by the Bromsgrove Standard, he said he did not believe the aide's trip to County Durham was "necessary or justified".
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He said he was "deeply sorry for all the hurt and pain and anxiety that people have been going through throughout this period", but repeatedly insisted it was now time to "move on".
Wednesday's session was the first time the prime minister has faced questions from MPs since the allegations against Mr Cummings emerged at the end of last week.
"However, in the same circumstances, none of us would have made the decisions he made - particularly over the visit to Barnard Castle".
"Here's the problem, Prime Minister".
Two more COVID-19 related deaths reported in Calhoun County
The Indian state of Maharashtra , the epicentre of COVID-19 positive cases, is still undecided about allowing air travel. In the worst affected state of the country, Maharashtra , the tally is dangerously close to crossing the 50,000 mark.
She did not call for Mr Cummings to be sacked - but apologised for the way the past few days have "undermined key public health messages".
Mr Johnson will face around 20 minutes of questioning on the Cummings row during his appearance before the Liaison Committee, a panel made up of select committee chairmen and women. Cummings has defended his actions, saying he traveled to ensure that his 4-year-old son could be looked after if he and his wife, who both had coronavirus symptoms, became sick.
Eight more Covid-19 deaths in Powys
Another 141 people have tested positive for Covid-19, bringing the total number of confirmed cases in the country to 13,556. On 9 May there were 214 deaths in care homes: 51% of the total, while 191 (46%) happened in hospitals.