Mrs Leadsom made the comments when she addressed the Conservative party conference in Birmingham on Monday (3 October).
"We want to make the most of this vast economic potential, as well as making sure there is a great quality of life on offer to those who live in rural areas," she said.
"I want people living in our market towns and villages to have the same life opportunities as those who live in our cities."
This should apply to school leavers looking for apprenticeships, single working mothers seeking access to free childcare and elderly couples needing local transport, she suggested.
Mrs Leadsom said the government's plan aimed to keep villages "thriving and growing".
She said she was also determined to improve mobile phone coverage and to roll out superfast broadband.
"I know so well how frustrating it is to search the house just for a single bar of signal when you're trying to send a text.
"Or worse still, if you can't get on to your Pokemon Go account."
Covering a range of subjects, Mrs Leadsom said building resilience was key to the success of the rural economy.
This was nowhere more so than in protecting communities from the impacts of increasingly extreme weather, including winter floods.
"The maintenance and improvement of flood defences across the whole country is crucial.
"That's why we are spending a record £2.5bn on 1,500 schemes, which will better protect 300,000 homes."
"We'll also be investing £1bn in flood maintenance over the course of this Parliament."
On agriculture, Mrs Leadsom said food and farming was of huge economic importance, generating over £100 billion a year and employing 1 in 8 of us.
"It is, in fact, our biggest manufacturing sector, bigger than the car and aerospace industries combined."
Brexit was a "superb opportunity" to establish new global trading relationships, including for British food and drink, which was worth more than £18bn in exports last year.
On the environment, Mrs Leadsom said it was "pretty shocking" that in the past year one in nine children hadn't visited a single green space.
"Yet we know two thirds of people live within 30 minutes of a National Park or Area of Outstanding Natural Beauty.
"Our plans set out how we want to engage children at every stage of their education, introducing them to the wonder of the great outdoors."
The government was also making great progress on the English Coastal Path – a 3,000 mile footpath extending around the English coastline, opening up the countryside.