The new leader earlier tried to dampen speculation he could call an early election.
The former mayor of London, who only took charge on Wednesday, has promised to take Britain out of the EU by the latest deadline of October 31 -- deal or no deal.
But he has focused on domestic priorities in his first few days in office, including a pledge on Friday to reverse drastic cuts to the police force made under May.
Commentators have speculated that he could be preparing to call a general election, hoping to regain the Conservative majority that May lost at the polls in 2017.
Johnson on Friday "absolutely" ruled out initiating such a poll before Britain leaves the bloc.
"The British people voted in 2015, in 2016, in 2017," he said during a visit to the central English city of Birmingham.
"What they want us to do is deliver on their mandate, come out of the EU on October 31.
"They don't want another electoral event, they don't want a referendum, they don't want a general election."
However, Britons could be headed to the polls if MPs bring down Johnson's new government in a no confidence vote in order to try and prevent a no-deal Brexit from happening.
Britain voted 52 percent in favour of leaving the European Union in a shock 2016 referendum that partially reflected deep resentment over economic inequality.
Johnson said Saturday's speech intended to "set out his vision to rebalance power, growth and productivity across the UK".
May also came to power promising to fight Britain's "burning injustices" but her domestic agenda was overwhelmed by Brexit negotiations and her failed attempts to persuade parliament to vote in favour of her exit deal.
Asked about the prospect of Brexit negotiations, Johnson said he was willing to engage with EU partners but only if the backstop clause was removed from the current divorce agreement struck by May.