An additional £10.1bn is needed annually to help local authorities in England plug funding gaps and improve services, council leaders say.
The Local Government Association said the figure included more than £5bn to ensure councils can maintain services at current levels, amid uncertainty caused by coronavirus.
It said £1.9bn was needed for increased demand in areas such as homelessness.
It came as the government geared up to set budgets for the coming years.
The figures were included in the Local Government Association's submission to the comprehensive spending review, which establishes the shape of government funding.
Chair of the association, Cllr James Jamieson, said the review would "shape the direction of this country for years to come" adding "securing the immediate and long-term sustainability of local services must be the top priority".
"With the right funding and freedoms, councils can improve the lives of their residents, address the stark inequalities the pandemic has exposed, develop a green recovery, address skills gaps and rebuild the economy so that it benefits everyone."
The LGA, which represents councils in England as well as the London boroughs, urged Chancellor Rishi Sunak to provide the additional core funding to councils in England by 2023-24.
It said the £5.3bn was needed to make up funding gaps and enable councils to maintain services - and warned this figure could double due to uncertainty caused by the pandemic.
A total of £1.9bn would go towards services struggling under increased demand, such as children's social care and homelessness.
And a further £2.9bn would enable councils to "play a leading role in helping communities recover and rebuild after the pandemic", the LGA said. This would include investment in reforming adult social care pay, boosting connectivity and improving parks.
The pandemic has increased the financial pressure on councils as demand for their services such as social care grow, while income from local taxation and charges has fallen.
Earlier this year some of the largest councils warned they could face bankruptcy without financial support.
During March and April 2020, the government provided £3.2bn to councils in emergency funding to help deal with the coronavirus pandemic.