Chris Grayling said investors now have two months to work up proposals which are financially credible without government support.
A new southern rail link to Heathrow Airport will be one of the first projects of this kind, with "third parties" such as local authorities and private sector companies invited to invest in the network.
Train disruption ahead as union confirms Yorkshire rail strike days next weekThe new market-led schemes will come on top of the Â£47 billion being invested in railways by the Government over the next five years.
The ideas would need to make commercial sense and fulfill passengers' needs without an over-arching need for public support.
Mr Grayling said: "We are investing in the most significant modernisation of the UK rail network since Victorian times, and I want the knowledge and expertise of investors and local partners to contribute to delivering new connections, more services and better journeys for passengers.
"This has already proved effective on a number of roads schemes in the UK. By encouraging innovative ideas and new investment on our railways, we can relieve the burden on taxpayers and fare payers with projects that match our transport needs. This can also support our economic and housing aspirations to ensure everyone benefits from an enhanced rail network.
"Heathrow is a perfect example of where this can make a real difference. Such schemes will help ensure the benefits of our major international hub are even more accessible to those across the west and south of the UK, providing vital links for travellers and exporters and attracting inward investment."
Shadow transport secretary Andy McDonald said: "Given the private sector’s poor record of investing in rail infrastructure, Chris Grayling’s plan is optimistic to say the least.
“As yet, there is no cost estimate or timeframe for the project. Labour supports improving surface access to our airports but issuing an invitation for investors is a far cry from a commitment.
“Following a series of recent outsourcing failures - including the collapse of Carillion and the Transport Secretary’s Â£2 billion bailout of failing train companies- these plans clearly aren’t in the best interest of taxpayers and passengers.
“Chris Grayling should focus on closing the North South divide in Transport spending by delivering the TransPennine electrification and matching Labour’s Â£10bn+ commitment to Crossrail for the North”