WASHINGTON — The Obama administration on Friday proposed cuts in Medicare payment rates for managed-care plans serving more than one-fourth of all beneficiaries, and Republicans immediately pounced on the proposal, which appears likely to become a significant issue in this year’s midterm elections.

The proposed reductions were larger than the administration had indicated in guidance given to the insurance industry in December. Jonathan Blum, a top Medicare official, cited the “historically low growth in Medicare per capita spending” as a reason for the proposal.

But Republicans said beneficiaries would suffer as a result of the cuts, which they traced to the Affordable Care Act.

“America’s seniors are feeling the brunt of Obamacare’s tax increases and cuts to Medicare,” said Senator Mitch McConnell of Kentucky, the Republican leader. Representative Dave Camp, Republican of Michigan and chairman of the Ways and Means Committee, said, “Millions of seniors who rely on the Medicare Advantage program will lose the plans, benefits, doctors and financial protection they currently have.”