By Hilary Russ

NEW YORK (Reuters) - Proposals in Congress that would effectively end Medicaid expansion in 31 U.S. states would cost those states at least $32 billion altogether in 2019, according to a report released on Friday.

"Few, if any, states could absorb such new costs," the Center on Budget and Policy Priorities, a Washington-based, left-leaning think tank, said in its report.

Republican President Donald Trump has pushed to fulfill a campaign promise to replace Obamacare, his Democratic predecessor's signature healthcare plan, with the help of a Republican-controlled Congress.

More details of potential replacements by U.S. House Republicans for former President Barack Obama's Affordable Care Act emerged on Friday, though they have yet to agree on a single detailed policy proposal to repeal and replace the healthcare law.

One scenario to phase out enhanced federal funding would convert the current system, in which states share the cost of Medicaid enrollees with the federal government, into fixed payments, or block grants, sent to the states.

But that would dramatically affect the 31 states and the District of Columbia that chose to expand Medicaid, the government health insurance program for low-income Americans, and collect extra dollars that came with expansion.

Those states would have to find the extra $32 billion themselves to maintain their expansions, the center said in its report.

The block grant conversion would "shrink federal Medicaid funding over time, result in even deeper funding cuts when needs increase, and ultimately place coverage for tens of millions more Americans at risk," the center said in its report.

The reduced federal funding would cause the automatic end of the expansion in seven states. Other expansion states would "almost certainly drop or substantially scale back their expansions," the report said.

Medicaid sits at the heart of the federal-state fiscal relationship. Over $330 billion in federal Medicaid dollars flowed to states in fiscal year 2016, accounting for more than half of all federal grants sent to state and local governments and the largest individual program, according to Standard & Poor's.

(Reporting by Hilary Russ; Editing by Jonathan Oatis)