In committing to the Office of Rail Regulation (ORR) plans, NR will also aim to bring down the costs of running the railways by 20% for the five-year period starting in April 2014.
NR will have to meet a target of running 90% of trains on time on London, south east England, regional and Scottish services and improving reliability on long-distance trains.
The company is also signing up to improved standards of infrastructure management, network resilience, and safety for passengers and railway workers.
Over the next five years NR will spend more than £38 billion on maintaining, renewing and improving the rail network.
ORR chief executive Richard Price said: "NR has committed to the challenge of delivering exciting plans for Britain's railways between 2014 and 2019.
"Service standards will get better, as stations up and down the country are modernised and lines are electrified. Alongside this work, the company will also deliver more, pound-for-pound, than ever before, as it utilises new technology and better ways of working."
Mr Price went on: "We welcome NR's recognition that it will need to do things differently to fully deliver. This is a fresh start for the company and an opportunity - supported by significant levels of funding by governments and passengers, and working with the rest of the industry - to learn lessons and build on successes from the past.
"Meeting these challenges will be tough, particularly in the early years for punctuality in England and Wales because of recent performance levels. We will focus on ensuring the company, working with governments and the rest of the sector, delivers its plans to achieve long-term and sustainable improvements for customers and taxpayers."
Michael Roberts, director general of industry body the Rail Delivery Group, said: "The multibillion-pound funding settlement for the railway for the next five years is vital to improving services and carrying more passengers and goods.
"Meeting the challenging targets on performance and efficiency will call for all parts of the industry to work more effectively together. We are committed to playing our part in making this happen."
NR's chief executive Sir David Higgins, who is leaving the company having become the new head of HS2 Ltd, said NR was disappointed that it was starting the 2014-19 period with train punctuality lower than the targets set for 2009-14.
He went on: "This is partly because of the weather but we also recognise our responsibility for the missed targets. We can still meet the targets for the end of the control period (2014-19). Although we cannot do so as quickly as assumed or in all weather, we will work with operators to improve performance as fast as possible."
Sir David added: "The railway is a complex, long-term, critical element of Britain's infrastructure and needs sustained, high levels of investment if we are to meet the public's rapidly increasing appetite for rail travel, and businesses' desire to move freight off congested roads."
"We were clear in the development of our plans that we would need to do some things very differently in CP5 (control period 5 from 2014-19) if we are to be successful in meeting the new challenges that we face and we remain committed to continuing with these changes
"Together with the ORR, we are determined to continue our drive to improve safety. Fundamental to this will be on-going improvements to our safety culture and how we manage our assets. By achieving this we can also deliver on-going efficiency savings and improve the reliability of train services, but getting the balance right between running more trains and improving punctuality will be a major challenge.".