The Telegraph reported the gatherings were made up of around 30 people drinking alcohol and dancing to music until the early hours.
Restrictions at the time banned indoor mixing between different households.
No 10 has not denied the events took place on 16 April 2021.
A spokeswoman confirmed Boris Johnson's former director of communications, James Slack, "gave a farewell speech" to thank colleagues ahead of taking up a new role as deputy editor of The Sun newspaper.
Mr Johnson was not at either gathering as he was spending the weekend at his country estate, Chequers.
The latest revelations come as he faces anger from his own party over attending a drinks gathering in the Downing Street garden during the first lockdown.
Labour's deputy leader, Angela Rayner, said "the buck stops with the PM" over the "culture and behaviours" inside No 10.
According to the Telegraph, Mr Slack's leaving party coincided with another gathering in the No 10 basement for one of the PM's personal photographers.
The reported events were held at a time when the UK was in a period of national mourning, which ran from 9 April to 17 April, following Prince Philip's death.
The Telegraph said staff were sent to a nearby shop with a suitcase, that was brought back "filled with bottles of wine".
During the basement gathering, sources claimed there was a "party atmosphere", with a laptop placed on a photocopier with "music blaring out".
The two parties are then said to have joined together in the No 10 garden and continued past midnight.
At the time, England was under 'step two' restrictions which stipulated that people could not socialise indoors, except with those from their household or support bubble. People could socialise outdoors in groups of up to six people or two households.
Other restrictions at the time included pubs and restaurants only being allowed to serve customers outside.
A Downing Street spokeswoman said Mr Slack "gave a farewell speech to thank each team for the work they had done to support him, both those who had to be in the office for work and on a screen for those working from home".
But asked about the other party and whether drinking and dancing had taken place, she said No 10 had "nothing further to add".
Ms Rayner said: "The Queen sat alone in mourning like so many did at the time with personal trauma and sacrifice to keep to the rules in the national interest.
"I have no words for the culture and behaviours at No 10 and the buck stops with the PM."
The leader of the Liberal Democrats, Sir Ed Davey, also reiterated calls for the prime minister to resign over the growing list of parties, tweeting: "The Queen sitting alone, mourning the loss of her husband, was the defining image of lockdown.
"Not because she is the Queen, but because she was just another person, mourning alone like too many others.
"Whilst she mourned, No 10 partied."
Fran Hall, from Covid-19 Bereaved Families for Justice, said: "If your neighbours had behaved like this, you'd have been disgusted. For the people running the country to do it and then lie about it shows a complete disdain for the general public."
This latest report adds to the growing list of alleged parties said to have taken place in Downing Street and other government departments during the pandemic.
But Mr Johnson has faced particular criticism after it emerged he had attended one on 20 May 2020 during the first lockdown.
The prime minister apologised on Wednesday in the House of Commons, saying he had joined staff for 25 minutes to thank them for their hard work. But he said he had "believed implicitly that this was a work event".
On Thursday, backbencher Andrew Bridgen became the fifth Conservative MP to publicly say they had submitted a letter of no confidence in Mr Johnson.
He told BBC Newsnight he had submitted the letter with a "heavy heart", believing there was no sign the revelations about parties in Downing Street during lockdown would end soon.
Mr Bridgen, who backed Mr Johnson in the 2019 Conservative leadership contest, said this was "preventing the government from functioning as normal and that's an untenable position".
A minimum of 54 Conservative MPs must send letters to the 1922 committee of backbench MPs in order to trigger a leadership challenge.
Chris Philp, minister for technology and the digital economy, said it was right to wait for the findings of senior civil servant's Sue Gray's investigation into reported parties at Downing Street and Whitehall.
He told Newsnight: "I think the public deserve to have a proper investigation with the full facts."