WASHINGTON—House Republicans released their plan to cut Medicaid spending, with the program’s defenders in the GOP appearing to win the intraparty clash over how aggressively to change the system that provides health insurance to more than 70 million low-income and disabled people.

President Donald Trump and House Republicans met to wrangle over one of the thorniest issues dividing the party: whether to cut Medicaid benefits for millions of low-income Americans.

House Republicans appear to be backing off some, but not all, of the steep reductions to the Medicaid program as part of their big tax breaks bill.