The former Chancellor, who is up against Liz Truss in the Conservative Leadership contest, was speaking to the Shropshire Star at a hustings event at Ludlow Racecourse on Wednesday.
Asked whether he would pledge support for Shropshire Council's £104 million levelling up bid, and if he would ensure the county doesn't feel overlooked and taken for granted, Mr Sunak said: "I want to make sure that particularly rural communities like Shropshire similar to mine in North Yorkshire do feel valued and recognised by central government down in Westminster, which I appreciate as a rural area like Shropshire, doesn't always feel like it's happening.
"Rural communities have particular needs and it's right that we recognise those. Whether that's support in farming, better broadband in rural areas or indeed recognising some of the funding challenges because of having to operate public services in a place where people are more spread out.
"These are all things I am intimately aware of, coming from North Yorkshire.
"I can assure you that any government I am privileged enough to lead will be very focused on rural communities like Shropshire and will make sure they get the support they need and the recognition they deserve."
Mr Sunak was also asked about catastrophic ambulance delays at Royal Shrewsbury Hospital and Princess Royal Hospital, and what he would do as leader to combat the problem.
His response was to discuss the NHS in broader terms, saying: "The NHS is incredibly important to me. I was brought up in an NHS family.
"Having seen what happened during the pandemic as Chancellor I did something that wasn't easy but I thought it was the right thing to do and that was to create a new way to raise money to fund the NHS properly, and indeed social care, so I think people can feel assured that the NHS is safe in my hands and it's a priority for me, given I've taken those decisions.
"I've set out a comprehensive plan to get to grips with some of the challenges within the NHS because we need to focus not just on the money we're putting in but the services we're getting out. That means reforming how we do things. It means using more technology to reduce the amount of management time that is currently there, focus resources on the front line. Be tough on people who are missing appointments because that will free up capacity in the system.
"And change the way we structure the NHS, whether that's elective surgical hubs, diagnostic centres, all things we can do to improve the productivity and the quality of the care we get. That's the plan we're going to put in place, I'm going to do it in the first 100 days because it is an incredibly important priority to me."
Asked how he would rebuild the party's reputation in North Shropshire after the damaging defeat in December, he said: "All the evidence shows that I'm the candidate that is best placed to appeal to swing voters everywhere. Not just winning back North Shropshire, which of course we have to do, but also across the country - Wales, Scotland, in the north and the south.
"In Liberal-leaning areas and Labour-leaning areas, I am the candidate that gives us the best opportunity to win and ensure that we win the next general election which is what I want our members to think hard about."