Downing Street said Dominic Cummings believed he "behaved reasonably and legally" when travelling from his London home to Country Durham during the lockdown.
Reports emerged on Friday saying the senior aide to Prime Minister Boris Johnson had travelled to his parents' home in Durham in breach of the UK Government's own lockdown rules.
Mr Cummings started suffering from coronavirus at the end of March and self-isolated with his wife, journalist Mary Wakefield, and young son for 14 days.
Downing Street said he was in his London home - and afterwards his wife wrote about “emerging from quarantine” into the London lockdown.
But a joint investigation by the Mirror and the Guardian suggests that Mr Cummings was in fact in the North of England.
Opposition MPs have accused Number 10 of a "cover-up" and called for the Prime Minister's top aide to resign after it emerged that he had driven 260-miles despite the guidelines on travelling.
But in a statement Downing Street said his actions were in line with guidelines and said reports that his family were spoken to by police were incorrect.
A Number 10 spokesman said on Saturday morning: "Owing to his wife being infected with suspected coronavirus and the high likelihood that he would himself become unwell, it was essential for Dominic Cummings to ensure his young child could be properly cared for.
"His sister and nieces had volunteered to help so he went to a house near to but separate from his extended family in case their help was needed.
"His sister shopped for the family and left everything outside.
"At no stage was he or his family spoken to by the police about this matter, as is being reported.
"His actions were in line with coronavirus guidelines. Mr Cummings believes he behaved reasonably and legally."
According to a joint investigation by the Guardian and Daily Mirror, Mr Cummings was spotted twice in the North East over the course of almost a week, between March 31 and April 5 - eight days after lockdown began.
Durham Constabulary said in a statement on Friday that officers attended a property in County Durham on March 31, more than a week after the lockdown had been imposed by the PM.
A spokesman said: "On Tuesday, March 31, our officers were made aware of reports that an individual had travelled from London to Durham and was present at an address in the city.
"Officers made contact with the owners of that address who confirmed that the individual in question was present and was self-isolating in part of the house.
"In line with national policing guidance, officers explained to the family the arrangements around self-isolation guidelines and reiterated the appropriate advice around essential travel."
Minister for the Cabinet Office Michael Gove has spoken out on behalf of Mr Cummings, tweeting: "Caring for your wife and child is not a crime."
Foreign Secretary Dominic Raab, responding to the Number 10 statement looking to explain Mr Cummings' reason for travelling during the lockdown, said an explanation had now been provided.
He tweeted: "It's reasonable and fair to ask for an explanation on this.
"And it has been provided: two parents with coronavirus, were anxiously taking care of their young child.
"Those now seeking to politicise it should take a long hard look in the mirror."
The SNP's Westminster leader Ian Blackford, in an interview earlier on Saturday, said there were "serious questions" for Mr Johnson to answer.
Speaking to BBC Radio 4's Today programme, Mr Blackford said: "What I find interesting is that (according to reports) members of Downing Street knew about this so, first and foremost, Boris Johnson has serious questions to answer over what now appears to be a cover-up.
"The Prime Minister must explain exactly when he knew about the breaking of the rules, whether he sanctioned it, why Cummings wasn't sacked immediately and why it appears that he tried to cover it up, not telling the public until the newspaper(s) broke the story, eight weeks later, last night."
Similar examples of public officials ignoring lockdown guidelines have led to resignations and condemnation from senior Tories.
When Professor Neil Ferguson, the epidemiologist whose modelling prompted the lockdown, quit as a member of the Scientific Advisory Group for Emergencies (Sage) for flouting distancing rules when he was visited by his girlfriend, Health Secretary Matt Hancock said he was "speechless".
Government guidance strongly urges people to stay away from the elderly during the pandemic, classing those over 70 as a vulnerable group.
