Under current rules, savers are not permitted to touch their pension savings until they reach age 55.
But the firm urged the government to rethink this rule, claiming allowing early access for a house deposit would increase younger savers' engagement with their pension.
Hargreaves included the call as part of its submission to the government's auto-enrolment review.
Nathan Long, senior pension analyst at Hargreaves Lansdown, said it was "crucial" that savers engage with their pension early, but said for younger people "the appeal of that first step on the housing ladder leaves pensions starved of attention".
"Limited early access to pensions to buy a first home will engage younger workers with pensions and investing for their future," he said.
The call comes two weeks before the firm is due to launch a Lifetime Isa, a tax-efficient savings vehicle which will serve the dual purpose of helping people saving for a first home and for retirement.
Many in the industry view the Lifetime Isa as a threat to auto-enrolment, and Hargreaves is one of the few providers that has committed to offering one.
In its submission, Hargreaves called for a number of other reforms to the auto-enrolment system.
These included allowing members to pick which pension scheme their employer pays into. Currently, the employer chooses the scheme, meaning people who work at a large number of different employers end up with a large number of different pensions.
The submission also called for the self-employed to be auto-enrolled by taking collecting contributions through their tax returns.
It also called for the earnings threshold for auto-enrolment to be set at the same amount as the new state pension - £8,090 a year, rather than the current threshold of £10,000.
Hargreaves also called for members to accrue pension contributions from "from the first pound they earn", rather than on a band of earnings between £5,876 and £45,000, as is currently the case.
The firm also called on the Department for Work and Pensions "put in place a comprehensive system to record data on those choosing to opt-out of auto-enrolment as well as those who cease contributing".
It claimed this evidence would be "critical" in determining how to increase minimum contributions and how this increase should be divided between employees and employers.
"A greater proportion of low paid, part-time workers are women and it is they and the self-employed that are the big losers under the current policy," Mr Long said.
"We cannot continue with this patchwork quilt of saving, people simply must be saving for their life after work. Lowering the amount you need to earn before being enrolled and sweeping up the self-employed as part of the tax return will include parts of the labour market that have until now been ignored."
The government launched the review of auto-enrolment last year, with a view to publishing recommendations for improving the scheme towards the end of 2017.
james.fernyhough@ft.com
