It comes as the Tory leadership contest schedule is due to be announced later today
Speaking for the first time since stepping down as Conservative leader last week, Mr Johnson said the party needed to move on quickly so government could focus “on the people” of the UK.
Boris Johnson has said he is “determined” to fulfill the mandate for which he was elected in the 2019 election as he prepares to spend his final weeks as Prime Minister.
“I am determined to go ahead and fulfill the mandate given to us, but my job is really just to oversee the process over the next few weeks and I am sure the outcome will be good,” he said.
“We just have to keep going, and like I said before, I think the more we focus on the people, on the people who choose us, on their jobs, on their aspirations and on what they can get out of investments in science and technology.
“The more we talk about the future we’re trying to build, the less we talk about politics in Westminster, the happier we’ll all be in general.”
The Prime Minister made the comments during a visit to the Francis Crick Institute, a biomedical research center in London today.
However, he did not specify which parts of the mandate he was referring to, nor did he clarify how he will carry his mandate through.
Instead, his comments appear to send a clear message to his successor to ensure the 2019 manifesto is presented ahead of the next general election.
Mr Johnson also refused to endorse any of the Tory MPs trying to replace him, saying: “It’s for the party to decide.”
He said whoever takes over as prime minister in the coming months will have a “great, great agenda” to go on with.
Mr Johnson also dodged questions about the Tory coup that led to his ouster, although he accused them of succumbing to a “herd mentality” in his resignation speech.
When asked if he felt betrayed by those who forced him to do this last week, he said: “I don’t want to say more about all of this.
“There’s a competition going on and it’s happening and I don’t want to spoil anyone’s chances by offering my support.”
It comes as Tory MPs release their bids to replace Mr Johnson. Eleven have signed up so far.
The competition will conclude today when the 1922 Committee of Backbench MPs meets to set the timeline for Boris Johnson’s replacement.
The committee sets the rules for the election, deciding when official nominations begin and end, the nomination threshold for voting, and the voting schedule.
MPs are likely to ensure the contest is narrowed down to the last two candidates before Parliament goes into the summer recess on Thursday July 21 – just 10 days away.
This story has been updated