Liverpool, Hull and Newcastle 'left behind' without HS2
Liverpool will be left behind without a dedicated connection to the HS2 rail route, a report commissioned by the city's mayor says.
The report by the think tank ResPublica said the link is essential if the Northern Powerhouse plan is to succeed.
It said cities like Hull, Liverpool and Newcastle could be put back "decades economically" without high-speed rail.
The proposed HS2 routes aim to cut journey times between London and northern England.
ResPublica said it could cost £3bn to extend HS2 to Liverpool.
It outlined that the city region fund could provide up to £2bn via a loan that would be repaid over 35 years.
Liverpool's mayor Joe Anderson, whose office commissioned the report, proposed the money come from "keeping hold of locally-raised taxes, rather than sending them to the Treasury".
ResPublica's proposal would see a dedicated high speed rail line linking the Liverpool City Region into the HS2 route to the north of Crewe, and connecting it to Manchester Airport and Manchester Piccadilly on high speed track.
This link in turn would also be the western most branch of the planned east-west "HS3" or "TransNorth" route running from Liverpool to Hull.
Director of ResPublica, Phillip Blond, said: "High speed rail offers a real chance to make the Northern Powerhouse work but it has to connect the cities of the north with each other, as well as London.
"If we don't extend the North South HS2 into an East West HS3 - the real benefits and gains from high speed rail will be lost.
"Both HS2 and HS3 could start in Liverpool and with the city able to find most of the funds there is no reason for the government to ignore this detailed and transformative proposal."
The government is developing a strategy looking at options, costs and a delivery timetable for HS3 before a report is produced in March.
A Department for Transport spokeswoman said HS2 was a "transformative transport investment that will benefit passengers across the North West, with high speed trains serving Liverpool from the day the Phase One route opens in 2026".
"This, together with our ambitious plans to transform east-west rail links through Northern Powerhouse Rail, will help deliver a rail revolution for Liverpool and the North."
The HS2 route from London to Crewe is expected to open in 2027 - with lines to Leeds and Manchester planned for completion in 2033.
Analysis: Arif Ansari, BBC North West Tonight political editor
Under current HS2 plans, passengers to Liverpool would only travel at high speed to Crewe before continuing their journey on existing lines.
Although the overall journey from London would be faster than it is at present, a trip to Manchester would be nearly 30 minutes shorter.
The ResPublica report is a plan to economically revitalise Liverpool and take advantage of the new metro mayor role in 2016.
It estimates that, if its 12 policy recommendations are accepted, the city could create up to 84,000 new jobs by 2030 - that includes 14,000 created by HS2.
It proposes that the city region is allowed to keep a larger share of the taxes raised through those new jobs and businesses. In addition, the city region would "capitalise" the Mersey tunnel tolls.
High speed trains would stop at an enhanced Liverpool Lime Street station and the same line would be used for the proposed HS3 service from Liverpool to Hull, although this would not actually run high speed trains.