The former Chancellor is widely believed to have been behind the scaling-back of plans for what was a flagship transport project last year.
Upgrades to existing lines, a new station in Bradford and an underground station at Manchester Piccadilly were also included in plans for project, which the Government said would cost around £36bn.
Mr Sunak said he agrees with the findings of a recent Transport Committee report, which said the Government should reasses its plan for Northern Powerhouse Rail (NPR) to ensure a "once-in-a-generation investment in rail is not to be a missed opportunity”.
He said he will "commit to engage with the local leaders in the North on delivering NPR" and "figure out the case for delivering a new station in Bradford".
He added: "I want to progress options to get HS2 two trains to Leeds as fast as possible and I've already committed the funding (£100m) to explore that further."
Ms Truss said delivering NPR in full is “absolutely crucial for the future of the North of England”, but she will not commit to reverting to the old plans for HS2 and ensuring the line reaches Leeds.
In November, the Government sparked a backlash when it announced scaled-back plans for NPR, which include a 40-mile line between Warrington and Marsden and a complete upgrade of the Transpennine Route.
In the Integrated Rail Plan, it said the original plan would cost £18bn more and cut journeys from Manchester to Leeds by just four minutes.
However, Northern leaders said it would transform the region’s outdated and overcrowded network by creating much-needed additional capacity and making services faster and more reliable.
During a visit to Leeds, Ms Truss said: “I have committed to Northern Powerhouse Rail going ahead.
“I will immediately, upon becoming Prime Minister, work with my new transport secretary and bring all the local groups together – the councils, the mayors and the MPs – to create a plan to move forward on this really important project.
“I’m clear it’s absolutely crucial for the future of the North of England.”
She added: “I also think the funding formula has been unfair on places like Leeds and places like Yorkshire so I will fix the Treasury funding formula to make sure that this part of the country is getting a fairer share of Government resources because frankly, transport is much better in London and the South East than it is here in Leeds, and I will fix that.”