The Centre for Social Justice (CSJ) think-tank, headed by Tory former leader Iain Duncan-Smith, said evidence suggests the UK is "not responding to the needs and potential" of an ageing workforce - with hundreds of thousands of people aged 50-64 deemed "economically inactive".
Its latest publication recommends helping older people "access the benefits of work" by providing support to them and employers, such as increased access to flexible working and training opportunities.
The report added if such support is implemented, it proposes an increase in the state pension age (SPA).
The SPA is set to increase to 67 by 2028 and to 68 between 2044 and 2046, although in 2017 the Government announced plans to increase it to 68 between 2037 and 2039.
The CSJ wants faster increases to the pension age, adding the cost of benefits would be reduced by employing more older people while it would boost the UK's gross domestic product (GDP).
In its report, Ageing Confidently: Supporting an ageing workforce, the think-tank states: "Removing barriers for older people to remain in work has the potential to contribute greatly to the health of individuals and the affordability of public services.
"Therefore, this paper argues for significant improvements in the support for older workers.
"This includes improved healthcare support, increased access to flexible working, better opportunities for training, an employer-led mid-life MOT and the implementation of an 'Age Confident' scheme.
"As we prepare for the future, we must prioritise increasing the opportunity to work for this demographic to reduce involuntary worklessness. For the vulnerable and marginalised, a job offers the first step away from state dependence, social marginalisation and personal destitution.
"In addition, provided that this support is in place, we propose an increase in the state pension age to 75 by 2035.
"While this might seem contrary to a long-standing compassionate attitude to an older generation that have paid their way in the world and deserve to be looked after, we do not believe it should be.
"Working longer has the potential to improve health and wellbeing, increase retirement savings and ensure the full functioning of public services for all."
CSJ chief executive Andy Cook said: "Right now, we are not doing enough to help older people stay in work and the state pension age doesn't even closely reflect healthy working life expectancy."
He added: "By increasing the state pension age, we can help people stay in gainful and life enhancing employment while also making a sound long-term financial decision."