Boris Johnson has said he will "absolutely" not call a general election before the latest Brexit deadline of 31 October.
Speaking during a visit in Birmingham, the prime minister said voters did not want another general election or a referendum.
"What they want us to do is deliver on their mandate to come out of the EU," he added.
Mr Johnson's comments come as he continues to appoint new ministers.
Asked whether he could provide an assurance an election would not take place before the end of October, Mr Johnson replied, "absolutely".
"We want to, and we are going to, deliver on the mandate of the people, which is to take the UK out of the EU whole and entire on 31 October," he said.
The new PM continues to make changes to lower-ranked jobs, following a radical overhaul of his cabinet on Wednesday.
Among the changes announced on Friday, Nick Hurd becomes a Northern Ireland minister, George Freeman has been given a transport brief, and Michael Ellis becomes the new solicitor general.
Tobias Ellwood lost his job as a defence minister, but said he would support Mr Johnson as a backbench MP and make the case for further defence spending.
'Minister for the Union'
Lord Bourne of Aberystwyth, who had been a junior housing minister and junior minister at the Wales Office, said he was quitting government over Mr Johnson's Brexit strategy.
He posted on Twitter that he had been asked to continue in both roles, but declined because "I cannot accept a no deal on 31 October".
Mr Johnson also confirmed he would change his own official title to include "Minister for the Union" - a pledge he made during his leadership campaign.
A Downing Street spokesperson said this was a "statement of his commitment" to strengthening ties between the constituent parts of the UK.
Boris Johnson's government
Who is in charge of what?
Other new appointments include:
- Baroness Goldie - defence minister
- Lord Ashton of Hyde - Lords chief whip
- Nadhim Zahawi - junior business minister
Those confirmed as remaining in their posts include:
- Kelly Tolhurst - junior business minister
- John Glen - economic secretary to the Treasury
- Chloe Smith - junior minister at the Cabinet Office
- Rebecca Pow - junior culture minister
- Nusrat Ghani - junior transport minister and assistant government whip
After appointing a new cabinet on Wednesday, with Sajid Javid as chancellor, Dominic Raab as foreign secretary and Priti Patel as home secretary, Mr Johnson began the complex job of reshuffling the rest of his government team.
Among a series of ministerial changes announced on Thursday, long-time ally Kit Malthouse was given a role taking over policing at the Home Office, and George Eustice returned to an environment brief.
Choosing a team is a hard job for prime ministers, with the possibility that those sacked - and those overlooked for a role - will become embittered.
On Thursday, former Brexit minister Steve Baker turned down a return to a junior job within the Department for Exiting the European Union.
The pro-Leave MP said he could not "repeat [his] experience of powerlessness" in the role.
With regret, I have turned down a ministerial job.— Steve Baker MP (@SteveBakerHW) July 25, 2019
I cannot repeat my experience of powerlessness as a junior @DExEUgov minister with the work done in @cabinetofficeuk.
I have total confidence in @BorisJohnson to take us out of the EU by 31 Oct.
Disaster awaits otherwise.
While Brexit Secretary Steven Barclay will nominally lead any future negotiations with the EU, most of the key work is expected to be done by No 10 and the Cabinet Office.
Michael Gove has been put in charge of overall planning for a no-deal Brexit, including its potential implications for Scotland, Wales and Northern Ireland.
As chancellor of the Duchy of Lancaster, a senior ministerial role without a specific portfolio, he will chair a number of key committees and taskforces.
Leaving his house for work on Friday, Mr Gove said Mr Johnson had "got a united cabinet and a united Conservative Party", adding: "The prime minister has got off to a fantastic start."
Margot James, who resigned as a culture minister earlier this month to back a bid to stop a future PM suspending Parliament to force through a no-deal Brexit, said Mr Johnson's appointments represented a "massive shift to the right".
In an interview with the Guardian, she said she could not have served under him because of his pledge to leave the EU by 31 October in all circumstances.
She added that she would not be able to campaign as a Tory candidate if the party went into a general election advocating a no-deal exit.
Asked if she could quit the party, she added: "I am really going one month at a time now. My goal is to make sure we leave in an orderly way with a negotiated settlement."
Under UK law, a government is allowed a maximum of 109 paid ministers, of which up to 23 can be full cabinet ministers - including the PM.
The Conservative Party currently has 311 MPs.
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