Jacob Rees-Mogg has suggested lockdown rules may have been too tough at the time the May 2020 drinks party took place in Downing Street.
He told MPs a future inquiry about Covid should look at whether "all those regulations were proportionate or whether it was too hard on people".
At the time, lockdown guidance said gatherings must be limited to two people outside.
The PM admitted he attended the drinks but believed it was a "work event".
Mr Johnson told MPs he had joined colleagues for drinks for around 25 minutes, to "thank groups of staff" for their hard work during the pandemic and apologised for his handling of the event, saying he understood people's "rage".
He is facing calls to quit from some senior Tories, as well as opposition parties, after admitting attending the party.
Commons leader Mr Rees-Mogg said: "I think everybody understands that people were obeying the rules and these rules were very hard for people to obey."
He told MPs that he had been contacted by a friend who was unable to go to the funeral of his two-year old granddaughter during lockdown.
"We must consider as this goes to an inquiry and we look into what happened with Covid whether all those regulations were proportionate or whether it was too hard on people," he added.
The public inquiry into Covid is set to begin work this spring. Baroness Heather Hallett was announced as the inquiry chair in December.
The prime minister's official spokesman said the government had sought to strike the right balance when introducing regulations and guidance.
"Clearly this was a unique situation in which we were required to move at speed and oftentimes whilst the evidence base was continuing to grow.
"We've sought to learn lessons throughout as we developed guidance in response to the pandemic over this period. But we're confident we sought to strike the right balance throughout."
He added: "I think prime minister has absolutely acknowledged that these restrictions do not...there is no cost-free option, both in allowing the virus to continue unimpeded and indeed introducing restrictions on people's way of lives and their livelihood."
The first coronavirus lockdown was introduced in England in late March and rules were slowly relaxed in May 2020, but it was not until 1 June that people were allowed to meet outside in groups of up to six people.
There were a number of legal restrictions in place in May 2020, including the law that people could not leave their homes - or be outside the place they live - without a reasonable excuse, which included work (where you couldn't work from home), exercise and getting things like food and medicine.
The gathering in Downing Street, described in the invitation as "socially distanced", was attended by around 30 people, who were invited to bring their own alcohol.
Mr Rees-Mogg also continued his criticism of the Scottish Conservative leader, Douglas Ross, who has called for the prime minister's resignation.
Mr Rees-Mogg dubbed the MSP and MP a "lightweight" on Wednesday, and said: "It seems to me that people who hold office ought to support the leader of the party, that is the honourable and proper thing to do."