Former Chancellor George Osborne has urged Theresa May to commit to building high-speed rail lines across the north of England, from Liverpool to Hull.
Mr Osborne said "HS3", which he had approved in government, would help the prime minister to "relaunch her premiership".
A "full-blown attempt to rebalance the economy of Britain" was needed, he added.
Greater Manchester Mayor Andy Burnham welcomed Mr Osborne's intervention.
But he added northern England would "speak for itself" on Wednesday at a transport summit for political and business leaders, in Leeds.
And a rail union accused the former chancellor of having presided over "cash-starved" services in the north of England during his time in government.
Mr Osborne launched the Northern Powerhouse project during his time at the Treasury, promising new funding and powers for cities, including Manchester, Liverpool and Leeds.
But, in Tuesday's Financial Times, he wrote there had since been a "systematic attempt" by Mrs May's advisers to "eradicate all mention of the initiative".
The Northern Powerhouse Partnership, which former Tatton MP Mr Osborne chairs, is launching a campaign for the new-high speed connection, starting with a line across the Pennines.
It was given the green light by Mr Osborne in his final Budget in 2016.
More than 70,000 people have signed a petition calling for Transport Secretary Chris Grayling to back the rail improvements, also called Northern Powerhouse Rail, and to give transport authorities in northern England the same powers as they have in London.
Mr Osborne admitted the project "will not be cheap", but said it would "transform" the economy.
Plans for "HS3" would follow on from the existing HS2 scheme - a planned line linking London and Birmingham that will split into two branches to Manchester and Leeds.
The partnership wants the government to redesign the second phase of HS2 to "remodel" four junctions, which could then be used for further connections under their proposals.
Mr Osborne said the new railway would "bring seven million extra people - and three times the number of businesses - within a 90-minute journey time of one of the northern cities".
He said the estimated cost of the Pennines line had been put as high as £7bn, but argued the investment could be spread over many years and the transport budget was built to take in such large projects.
"There is no geographical reason why this cannot happen," wrote Mr Osborne.
"The distance between Manchester and Leeds is shorter than the length of the Central line on the London Underground."
Speaking on BBC Radio 4's Today programme, he said the Northern Powerhouse idea was still "thriving".
"Now the idea is not just dependant on the political career of one chancellor or one prime minister, it exists and it breathes and it lives in the north of England."
Mr Osborne was sacked by Mrs May when she took office and has been a frequent critic of her government through the London Evening Standard newspaper, which he now edits.
In his FT article, he wrote: "Far be it from me to offer advice to the prime minister on how to relaunch her premiership this autumn, but making this big commitment to the North, at the Conservative conference in Manchester, would not be a bad place to start."
Please help strengthen our case by signing this petition. Memo to Govt: the North is getting organised! 2/2 https://t.co/mnWEyGQilT— Andy Burnham (@AndyBurnhamGM) August 21, 2017
Last year, the prime minister vowed to press ahead with the project.
Writing in the Yorkshire Post, Mrs May promised to "help the great cities and towns of the North pool their strengths and take on the world".
However, last month the government scrapped the planned electrification of railway lines in Wales, the Midlands and the north of England, prompting anger from local authorities and businesses.
Days later, Transport Secretary Chris Grayling backed proposals for Crossrail 2 - a north-east to south-west railway in London - sparking anger from political leaders outside the capital.
A spokesman for the Department for Transport said the government had already made a commitment to Northern Powerhouse Rail, giving £60m to Transport for the North to develop plans, adding: "[We] look forward to working with them once proposals are submitted later this year."
"We are also investing billions of pounds across the north of England to better connect communities, build the Northern Powerhouse, and deliver improved journeys right across the region," the spokesman said.
Rail, Maritime and Transport union general secretary Mick Cash accused Mr Osborne of "hypocrisy" over his comments.
He said: "This is a man who was the key player in governments which presided over fragmented, cash-starved and privatised rail across the North and which put profiteering first while passengers were left rammed into clapped-out, lashed-up Pacer trains."
Labour's shadow transport secretary Andy McDonald added: "Even George Osborne recognises that the Tories' chronic underinvestment in transport is holding the North back."