“I believe that in every respect he has acted responsibly and legally,” Mr Johnson told a news conference on Sunday (local time).
Mr Johnson said “some” of the allegations about Mr Cummings’ behaviour during self-isolation were “palpably false”.
Mr Cummings, who masterminded the 2016 campaign to leave the European Union, travelled 400km from London to Durham in late March while his wife showed COVID-19 symptoms, when measures to combat the spread of the coronavirus were in place.
Mr Johnson had ordered Britons to mostly stay at home and shut down large parts of the economy to curb the outbreak which has left the United Kingdom with one of the world’s highest official death tolls.
Mr Johnson’s office said Mr Cummings made the journey to ensure his four-year-old son could be properly cared for as his wife was ill with COVID-19 and there was a “high likelihood” that Mr Cummings would himself become unwell.
A number of cabinet ministers and the attorney general have also said that the journey was justified.
Several lawmakers from Johnson’s Conservative Party however called on Sunday morning for Mr Cummings to quit.
High profile Brexit campaigner Steve Baker, was the first of a number of Conservative lawmakers who said Mr Johnson’s adviser should now quit.
“I just see this rattling on now for day after day, wasting the public’s time, consuming political capital and diverting from the real issues we need to deal with,” he told Sky News.
“No one is indispensable.”
Opposition politicians have called for Mr Cummings, who wields huge influence on the government, to go, saying his actions were hypocritical at a time when millions of Britons were staying in their homes.