The government wants to reverse the effects of a court ruling which expands the number of people who can claim Personal Independence Payments.
The PM's official spokesman said the welfare system was a "strong safety net for those who are in need of it".
Meanwhile, a No 10 aide apologised for any offence after saying benefits should go to "really disabled people".
No 10 policy unit head George Freeman had faced calls to apologise after saying on Sunday those "taking pills at home, who suffer from anxiety" should not receive Personal Independence Payments.
On Monday he tweeted: "Having experienced myself traumatic anxiety as a child carer living w alcohol I know all too well the pain anxiety + depression causes...
"Which is why as a former health minister and policy adviser I am passionate about supporting mental health and disability, and hugely regret if my comment about the need to prioritise the most 'serious disabilities' inadvertently caused any offence which was not intended."
The prime minister's official spokesman said the Personal Independence Payments (PIP) reforms were not about saving money and said that about Â£50bn a year was spent on supporting people with disabilities and health conditions.
"The government has been clear on the parity of esteem we want to see between mental and physical health," the spokesman said.
"What we are doing now is restoring the original intention of the PIPs which was to make sure there was a sustainable benefit to provide continued support to those who face the greatest barrier to living independent lives."
Pressed on whether the prime minister had a message for those who could be affected by the changes, the spokesman said "nobody is losing out".
He said a recent tribunal on assessments for PIP payments had "broadened" the criteria.
The government is proposing changes to PIPs, which replaced the Disability Living Allowance, after tribunal rulings that claimants with psychological problems who cannot travel without help must be treated like those who are blind.
The government says the rulings - if unchallenged - would have added Â£3.7bn to the benefits bill by 2023.
The benefit is intended to help people cope with the extra costs of living with ill health or disability and are made according to the points a person scores in an assessment of their needs.
Disabilities minister Penny Mordaunt said she was reforming the PIP payments to "restore the original aim of the benefit" to make sure support was given to the most needy.
Shadow chancellor John McDonnell said he was "furious" about the proposed changes to PIPS, and said Labour would pressurise the government to reverse them in next month's Budget.
The Liberal Democrats said the government was using court losses "as an excuse to severely restrict disability benefits".
Downing Street has defended plans to change access to disability benefits, saying that "nobody is losing out".