The meeting of political and business officials in Leeds on Wednesday shows "the patience of people in the North of England has run out", he added.
It comes after a series of rail links in the North, Wales and Midlands were axed or downgraded as Government supports plans for a new Â£30 billion Crossrail 2 scheme in London and the South East.
But Transport Secretary Chris Grayling argued that, while improving northern transport links was one of his "biggest priorities", they must be "designed and managed by the North itself".
Writing in The Yorkshire Post, he said: "It is central government's responsibility to provide funding and a delivery structure that ensures efficiency, value for money and accountability.
"But, beyond this, I want the North to take control."
Mr Grayling sparked anger last month by supporting a new Â£30 billion Crossrail 2 scheme days after rowing back on upgrade plans for the North.
More than 83,000 people have signed a petition from the Institute for Public Policy Research (IPPR) North think-tank calling on Government to fund Crossrail for the North.
It made several demands of the Transport Secretary:
* An "immediate commitment" of at least Â£59 billion over the next decade in "catch-up cash" to close the gap on per-head public spending in London;
* His backing of the Northern Powerhouse Rail programme - including a "Crossrail North" 30-minute link between Manchester and Leeds;
* Transport for the North to get "the same powers as those enjoyed by Transport for London" so private finances can be raised.
The think-tank added: "Crossrail 2 was not in the Conservative Party manifesto - whereas Northern Powerhouse Rail was.
"This is not just a matter of fairness. This is not special pleading ... But lack of government spending on northern transport is holding the whole economy back. Northern prosperity is national prosperity."
Mr Burnham, who will speak at the summit, said: "We are not against our capital city developing world-class infrastructure but it cannot be at the expense of the North. People here have put up with clapped-out trains and congested roads for long enough.
"Today's event shows that the patience of people in the North of England has run out."
Leeds City Council leader Judith Blake said: "Transforming rail connections across the North was part of the original plan to create a Northern Powerhouse and was estimated to bring Â£100 billion in economic growth as well as 850,000 new jobs."
She added that failure to invest "would hold back the potential of the North for decades to come".
Leaders of Sheffield, Newcastle and Manchester councils, Liverpool City Region Metro Mayor Steve Rotheram and business representatives will be among delegates attending the conference.
Transport Minister Paul Maynard said funding had been provided for the development of detailed proposals for transport upgrades in which the Government could invest.
He said: "I keep hearing demands for investment in the North but I should point out they come from some of the very same people who we have asked to help develop plans.
"We all want to improve rail in the North and we are all getting on with the work that needs to be done."
Mr Burnham said there had to be a partnership and there was "no way" of delivering the infrastructure the North needed alone, as "substantial" Government investment was necessary.
He told BBC Radio 4's Today programme: "The Westminster system has failed the North of England, there is just no doubt about that, and that's under governments of all colours by the way, it's a London-centric system."
Devolution to the English regions, he said, represented the best chance of "breaking that cycle", adding: "The North has been at the back of the queue for too long."