The Transport Secretary Chris Grayling has conceded that there is a "big challenge' that needs to be addressed to improve Britain's railways.
It comes after a scathing report by MPs warned the current rail franchise model is 'no longer fit for purpose' and is failing passengers.
Grayling told the BBC's Andrew Marr Show railways are "bursting at the seams".
"The number of passengers have doubled, trains are full, we've crammed as many trains as we can on to many lines.
"That's the big challenge that we need to address," he added.
Grayling also said he agreed with a lot of the MPs' report: "It's made a series of sensible recommendations of how to improve things, many of which I'm already doing."
The Commons Transport Select Committee said private operators are restricted in how much they can improve services and efficiency.
It urged the Department for Transport (DfT) to commission an independent review of its franchising functions, including the possibility of transferring enforcement powers to the regulator the Office of Rail and Road.
The report added that although there can be no "single template" for franchises, there is "merit" in procuring longer agreements covering smaller areas.
The MPs said the relationship between Network Rail - which owns and manages rail infrastructure - and train operating companies (TOCs) is "not as coordinated as it should be", leading to higher fares and poor performance.
Transport Select Committee chairman Louise Ellman said passengers are suffering.
The committee concluded that a wide restructuring of the system would be "prohibitively impractical" because of the burden on resources and the restrictions of existing agreements.
Instead, it recommended that as contracts expire, the DfT should consider whether they should be modified to "align better with the specific market they serve".
At the time of privatisation in the 1990s there were 25 franchises, compared with just 15 today.
Leader of the Rail, Maritime and Transport union, Mick Cash, claimed rail franchising is a "fiasco" which should be replaced by a publicly owned railway that "puts people before profit".
The DfT said £40 billion is being spent on upgrading the railways and the franchising system has brought major investment to help create one of the safest and fastest growing networks in Europe.