Liverpool has offered to pay £2bn towards the cost of HS2 if the government agrees to add a 20-mile stretch of track that would bring the city into the planned high-speed rail network.

With the £55bn railway proposed to directly link Manchester and Leeds to Birmingham and London, Liverpool’s leaders fear the city will be left behind its counterparts in the north.

Liverpool’s offer would be a long-term repayment commitment – and depend largely on the accompanying devolution of resources normally paid direct to the Treasury, including local employers’ national insurance contributions.

However, politicians insisted that the proposals were credible and emphasised how the investment would pay dividends for Liverpool and the UK economy.

The mayor of Liverpool, Joe Anderson, and local MPs including Angela Eagle and Louise Ellman, the chair of the transport select committee, endorsed a report by the thinktank ResPublica that argued a high-speed link to Liverpool is essential for the success of the “northern powerhouse” envisioned by the chancellor, George Osborne.

The plan would see a dedicated high-speed line linking Liverpool to the HS2 route north of Crewe, connecting to Manchester and its airport. The link would form the western point of a HS3 route of fast east-west links across the cities of the north.

The report puts the cost of extending HS2 to Liverpool at £3bn and says the city could cover two thirds of that sum through increased revenue in business rates and employment that the line would stimulate over several decades.

Anderson said: “The need for Liverpool to be connected to both the other cities of the north and London is huge if we as a city are going to play our part in generating money, jobs and continued growth through the northern powerhouse.

“Our funding plan would make up the bulk of the price with £2bn coming from keeping hold of locally raised taxes, rather than sending them to the Treasury. Using this mechanism would allow both ourselves and the wider economy to move closer to prosperity.”

Anderson added that he saw no logistical problems in building a high-speed line to Liverpool, unlike in the south, which has seen residents from Camden and the Chilterns in particular campaign hard against the the first phase of HS2’s route. The extension would free up capacity on existing rail lines for freight, with millions more containers expected through the Liverpool2 port opening next month, he said.

“If we’re serious about rebalancing the economy there has to be a fairer distribution of infrastructure spend – all these Crossrails 2, 3 or 10 in London will probably happen before we get HS3. They’ve got to connect up the north,” said Anderson.

Profits from the Mersey tunnels could potentially be invested in the HS2 link, the report suggests, although Anderson said he would rather spend that money now because of how severely the city has been affected by central government cuts.

Anderson conceded that it might be difficult to sell Liverpool paying, however circumspectly, for a connection when Manchester’s track was funded centrally. But, he said: “That’s an issue of us showing how determined we are to have it. It’s actually to expose the failings of the government’s argument not to continue the line here: the economic case is clear. Is it going to be financially detrimental by being excluded? Yes, we are going to be disadvantaged.”

Ellman said the proposals were “well thought out and must be seriously considered.”

A detailed route for the second phase of HS2’s network to the north, due to be built between 2026 and 2033, is expected to be published later this year.

A spokesperson for HS2 Ltd said that the current proposals would see Liverpool benefit with two high-speed trains per hour compatible with existing tracks after the route connecting London and Birmingham is completed in 2016, making journeys from the capital half an hour faster.