David Cameron said a third high-speed rail line in the north, known as HS3, was about "connectivity" not just faster journey times.
"It's recognising that if we link up the great cities of the north of England they could become a northern powerhouse to rival the dominance of London," the Prime Minister said.
He added: "It's a fundamental rebalancing, it's part of our long-term economic plan and we're only able to do it because we've got a successful, growing economy."
The RMT union has said that it is "cynical in the extreme" that the government is "threatening to devastate jobs and services" whilst launching proposals for a third high speed rail link in the north of England.
Former deputy prime minister John Prescott has welcomed a report proposing a high speed rail link between Leeds and Manchester, but said his party first recommended the plans a decade ago.
Train journey times between northern English cities could be slashed by half after ministers backed plans for a third high-speed railway.
The proposals were put forward in a report from the head of the £50 billion HS2 high-speed rail project, Sir David Higgins.
The improvements would cover an east-west section of northern England and would be in addition to the north-of-Birmingham phase two of HS2 which will see a Y-shaped route going to Manchester and Leeds.
Sir David said northern connectivity plans - dubbed "HS3" and backed by Chancellor George Osborne - would be "as important to the north of England as Crossrail is for London".
If carried forward, the plans would mean journey times between Leeds and Manchester could almost be cut in half.
While journeys between Leeds and Birmingham, Leeds and Sheffield Meadowhall, York and Birmingham and Nottingham to Birmingham could also be reduced by a half or more, and many more journeys across the country substantially shortened.