Boris Johnson has backed his key adviser Dominic Cummings amid a row over the aide's travel during lockdown.
The PM said he believed Cummings had "no alternative" but to travel from London to the North East for childcare "when both he and his wife were about to be incapacitated by coronavirus".
"In every respect, he has acted responsibly, legally and with integrity," Johnson said.
It follows calls from several Tory MPs for Cummings' resignation.
Labour leader Sir Keir Starmer said Johnson's decision to take no action against Cummings was "an insult to sacrifices made by the British people".
Leaving Downing Street after about six hours in Number 10 on Sunday, Cummings refused to answer questions.
A tweet on the UK Civil Service official Twitter feed appeared to be a criticism of Johnson's stance.
It said - "Arrogant and offensive. Can you imagine working with these truth twisters?"
The tweet has since been deleted.
Meanwhile, Johnson said parents and teachers should prepare for the phased reopening of schools in England to start on 1 June as planned.
He also announced that a further 118 people had died with coronavirus in the UK, across all settings, bringing the total to 36,793.
On Saturday, Cummings and the government had said he acted "reasonably and legally" in response to the original claims that he drove about 420km from London to County Durham with his wife, who had coronavirus symptoms.
The aide then faced further allegations on Sunday of a second trip to the North East, reported by The Observer and Sunday Mirror.
Speaking at Downing Street's daily coronavirus briefing, Johnson called "some" of the claims "palpably false".
Johnson said he held "extensive" discussions on Sunday with Cummings, who he said "followed the instincts of every father and every parent - and I do not mark him down for that".
"Looking at the very severe childcare difficulties that presented themselves to Dominic Cummings and his family, I think that what they did was totally understandable - there's actually guidance... about what you need to do about the pressures that families face when they have childcare needs.
"He found those needs where they could best be served, best be delivered and yes, that did involve travel."
When asked whether Cummings made a trip to Barnard Castle - about 48 miles from Durham - during his isolation in April, Johnson said his aide isolated for 14 days and he was "content that in all periods and in both sides (of isolation) he behaved responsibly and correctly".
UK Labour had called for an urgent inquiry into the allegations, while several Conservative backbench MPs publicly questioned Cummings' position, including Sir Roger Gale.
Reacting to the prime minister's comments, Sir Roger said it was an "extraordinary position" for Johnson to take.
"It's up to the prime minister to exercise judgement about who he has around him," he told BBC Radio 5 Live.
"In this case, I do think that that judgement is flawed. I don't think many people will buy into the idea that suddenly after the event it's okay to reinterpret the rules".
Speaking to the BBC, Labour leader Sir Keir Starmer said: "This was a huge test of the prime minister and he has just failed that test.
"Millions of people across the country have made the most agonising choices - not visiting relatives, not going to funerals - they deserve better answers than they got from the prime minister today."
He also said he would have sacked Cummings if he were prime minister.