The two candidates hoping to take over from Boris Johnson are looking to woo Red Wall voters in the first of 12 party faithful sessions.
With hustings taking place across the country, the membership will quiz the final two candidates before voting for the next party leader and prime minister closes on September 2.
The winner will be confirmed by September 5.
Thursday evening's event takes place in Leeds, where Ms Truss was hoping to shore up voters’ support by backing Northern Powerhouse Rail in full and pledging to “turbocharge investment” into the north of England.
Rishi Sunak speaking at an event in Newmarket
Joe Giddens
Liz Truss with supporters at an event in Leeds
Henry Nicholls
During a visit to the Yorkshire city, Ms Truss insisted she is “completely committed” to the scheme to improve rail connections between Liverpool and Leeds, which was originally announced by Mr Johnson but subsequently scaled back.
She said: “I grew up in Leeds, I know how poor the transport is and frankly, it’s not got much better since I was a teenager getting the bus into Leeds city centre.
“What I want to see is really fantastic rail services, better roads so people are able to get into work."
Asked how she would afford the scheme, Ms Truss said: “The taxes that I am cutting are affordable within our budget.
“By creating new low tax investment zones in places like West Yorkshire, by enabling the post-Brexit reforms to take place, unleashing more investment from the city, we will grow the economy faster – that will bring in more tax revenue, and that will enable us to afford those projects."
Louise Haigh, Labour's Shadow Transport Secretary, accused Ms Truss of offering only “weasel words” on delivering new lines.
But the Foreign Secretary’s campaign was also buoyed by the endorsement of Jake Berry, leader of the Northern Research Group (NRG) of Tory MPs.
He described her as “the person with energy to bring action and delivery to make sure that we level up our United Kingdom”.
Ms Truss is doing well in opinion polls – but Mr Sunak has a significant edge over his rival among swing voters – 2019 Tory voters who are deserting the party.
Mr Sunak is seeking to regain his footing after he was accused of “flip-flopping” on his fiscal policy, as he pledged to temporarily slash VAT on energy bills despite repeatedly branding Ms Truss’s tax-cutting plans as “comforting fairy tales”.
In his latest policy announcement, Mr Sunak said he would protect the “precious” green belt as he argued more homes can be built on brownfield sites.
Mr Sunak, who admitted he is the “underdog” in the contest an interview with Conservative Home, was praised for his “very good judgment” by senior supporter George Eustice.
Rishi Sunak delivers a speech at Vaculug tyre specialists at Gonerby Hill Foot, Grantham, as part of his campaign to be leader of the Conservative Party
Danny Lawson
Rishi Sunak and Liz Truss before taking part in the Tory leadership debate, held in Stoke-on-Trent
Jacob King
The Environment Secretary told Sky News: “I think that’s what our country needs as we try to chart our way out of these difficult times”.
And former chief whip Mark Harper, another ally of Mr Sunak, defended the ex-Chancellor’s decision to announce his pledge to cut VAT from domestic energy bills for a year at this stage in the race.
The hustings in Leeds comes as mayors from across the North of England have written to the two contenders to express concerns about the Government’s plans for northern transport.
Andy Burnham, Tracy Brabin, Steve Rotheram, Oliver Coppard and Jamie Driscoll called on the winning candidate to meet with them to agree a “better way forward for the North”.
They wrote: “This is a critical decision that will affect the lives of generations of Northerners to come. We owe it to them to show the highest possible ambition for what the North of England can be in the future."