The annual White House budget, released Monday, also seeks to move more than $1 trillion in Medicaid spending to a system of block grants allowing states more control in allocating the funds, in addition to cutting another $1.5 trillion over the next 10 years.
Obama also curtailed payments to private insurers in Medicare Advantage, which Trump does not do.
Democratic leaders in both the House and the Senate pronounced the budget "dead" when it arrived on Sunday evening.
House Democrats are working on their own budget proposal that would be a blueprint for setting spending levels.
The analysis from the nonprofit Committee for a Responsible Federal Budget shows most of the Medicare cuts the president proposed "come from policies which would reduce, not increase, premiums and other out-of-pocket costs for seniors, and would do so without reducing the benefit offered by Medicare".
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The president's proposal also includes work requirements for Medicaid recipients, and it would convert Medicaid to a state-administered program supported by federal block grants.
Trump's proposals met with immediate criticism from the host of candidates for the Democratic presidential nomination. The Trump administration is promoting work mandates and has approved requests from eight states to add it to their programs. Oral arguments in lawsuits against the programs in Arkansas and Kentucky begin later this week.
He cast the proposed cut as the president's attempt "to balance his books" after giving more than $2 trillion in tax cuts to major corporations and wealthy Americans. Multiple Democrats running for president in 2020 espouse some version of an expansion, lumped in popular discourse under the umbrella term of Medicare for all.
The head of a major hospital association pushed back hard, saying in a blog that "arbitrary and blunt" Medicare cuts would have a "devastating" impact on care for seniors. The cost-saving covers some of the mandatory programs such as Medicaid, Medicare, and programs on federal health care. "It is no time to gut Medicare".
The proposal also calls for reducing nondefense spending by 5 percent, which would include cuts to domestic programs such as Medicare, the Environmental Protection Agency and the Department of Education. The department's total gross discretionary funding would go down to $44.1 billion in 2020 from this year's $52.8 billion.
HHS secretary Alex Azar will appear in front of three separate Congressional committees this week to defend the budget: Tuesday, the House Energy and Commerce subcommittee on Health; Wednesday, the House Appropriations subcommittee; and Thursday the Senate Finance Committee.