It came as he launched a £6m Let’s Do London campaign to encourage Londoners to boost the capital’s economy by taking "staycation" breaks as the easing of the lockdown allows the reopening of cultural and entertainment venues.
In a message of conciliation, Mr Khan said at the signing-in ceremony at Shakespeare’s Globe: “The country and the city remain deeply divided. I pledge to use my second term to build the bridges to bring us closer together.
“As we recover and build from this pandemic, we simply must use this moment of national recovery to strive for a moment of national healing too.”
But he admitted he had his “work cut out” in his second term to restore the capital’s fortunes.
He vowed to “work day and night” to deliver “safer streets” saying: “On crime – we’ll continue to be both tough on crime and tough on the causes of crime. This includes putting even more police officers on the streets at the same time as investing record amounts in new opportunities for young Londoners.”
In his first media interview afterwards, he told the Standard: "The key thing is to make sure our city recovers. It’s the biggest challenge our city has faced since the Second World War, and that’s what Let’s Do London is about - getting our city back on its feet after the awful 15 months we have had, and try to bring our city together and our country together.
"We have got to avoid this culture war which is tearing our country apart. We have got to make sure we have the Brexit scars healing and we ought to try to bring pople together. My mission in the second term is to bring our city together."
He added: "We are making fantastic progress in defeating this virus. The vaccine rollout has gone fantastically well. Of course there are concerns about the Indian variant... but I’m optimistic.
"Next Monday restaurants will reopen, many theatres will reopen. On June 21, fingers crossed, our city will return to a semblance of normality. It’s going to be an amazing summer."
He was re-elected late on Saturday night after defeating Tory rival Shaun Bailey, but with a slightly smaller share of the first-preference vote. But he insisted he had a "decent mandate" overall, having secured more than 1.2m votes.
"I didn’t realise I secured the biggest vote ever received by a candidate, other than myself, of course, in 2016," he said. "But also I discovered I have got the biggest majority, other than myself in 2016. Quite a decent mandate, if I say so myself."
He backed Labour leader Sir Keir Starmer after a controversial reshuffle. He said Labour’s local election results outside London had been "mixed" and added: "Keir is right to make changes to make sure we can win back the trust and confidence across the country that we need to do.
"He sent me a really nice message over the weekend and I’m looking forward to helping the national party to show the difference Labour can make in London, and Andy Burnham and Steve Rotheram have already shown the difference we make across the country."
Major campaign to encourage Londoners to take a ‘staycation’
Visitors from across the UK were also being urged to return to central London, lured by a £6m Let’s Do London campaign promoting events from the delayed Euro 2020 football tournament to a David Hockney exhibition at the Royal Academy of Arts.
City Hall promised “the biggest domestic tourism campaign the capital has ever seen” to help London’s economy get back on its feet as Covid restrictions are eased.
There will be a series of one-off events, outdoor film screenings and late-night openings under the London Lates initiative to ease social distancing.
David Hockney, one of the UK’s most influential living artists, has redesigned the iconic Tube roundel as “Hockney Circus” in a special artwork that can be seen at Piccadilly Circus station from Monday.
The aim is to turn central London into a huge outdoor art gallery, with other exhibits including Asphalt Art by award-winning London designer Yinka Ilori.
Artist and designer Es Devlin will plant a living forest at Somerset House for this year’s London Design Biennale.
Road crossings and street furniture in the West End will be redesigned in a partnership involving Royal Academy artists.
London Fashion Week, Frieze London, the London Design Festival, and the 65th BFI London Film Festival will return in the autumn.
The Let’s Do London campaign will continue throughout the year urging Britons to consider the capital for mini-breaks rather than the countryside or beach.
Kate Nicholls, chief executive of UK Hospitality said: “The ‘Let’s Do London’ campaign is a shot in the arm to help revive the capital’s ravaged visitor economy.”
Actor Adrian Lester, who joined Mr Khan at the Globe, said: “This has been the toughest year in decades.
“As creative artists we depend enormously on our fans and the visitors who want to see us perform.”
Standing as “groundlings” at the Globe will initially be banned, with seating in the yard until July 4.
Neil Constable, chief executive of Shakespeare’s Globe, said: "From May 19 we reopen with A Midsummer Night’s Dream and we look forward to welcoming audiences in safely to enjoy the thrill of live theatre at last."