The House narrowly approved a far-reaching overhaul of the nation’s food-stamp program Thursday that would slash food aid to about 4 million Americans over the next few years and shift a greater burden of taking care of the poor to state governments.

The Republican-backed plan, which would cut about $39 billion in funding for food-stamp programs over the next decade, differs sharply from a bipartisan Senate proposal passed in June, and its passage is likely to further strain relations between the two chambers as they prepare to spend the next several weeks battling over a short-term budget deal and raising the federal debt limit.

The legislation passed Thursday is of a piece with the looming battles as it represents House Republicans’ effort to pare the cost and size of government by reducing federal spending.

Thursday’s vote represented a victory for House Majority Leader Eric Cantor (R-Va.), who embraced a strategy this summer that split apart the farm bill to consider funding for food stamps, formally known as the Supplemental Nutrition Assistance Program, separately from legislation authorizing crop subsidies and a revamping of many agricultural and conservation programs.

Cantor said the deep cuts enacted Thursday were necessary because while most SNAP recipients need the assistance, there are many people who abuse the system.

“Frankly, it’s wrong for hardworking, middle-class Americans to pay for that,” Cantor said.

Rep. Tim Huelskamp (R-Kan.), a strong supporter of the bill, said that stiffer work requirements for certain adults applying for SNAP funds mean “you can no longer sit on your couch . . . and expect the federal taxpayer to feed you.”

The House voted 217 to 210 to approve the measure. Fifteen Republicans joined with all of the Democrats present to vote against the plan.

Passage of the bill means that the House can begin negotiations with the Senate over a final version of the farm bill, which would once again merge food aid with other agricultural policy.

But Senate Majority Leader Harry M. Reid (D-Nev.) , in a long speech on the Senate floor Thursday, rejected the GOP approach, saying that Republicans had “turned their backs” on low-income families in hopes of making budget cuts.

Citing his own trips to the grocery store with his wife, Landra, Reid said that proposed reductions in SNAP funding would make it difficult for some recipients to purchase ground beef and milk in the same shopping trip.

In the House, Democrats used the hours before the vote to criticize Republicans for the funding reductions. They repeatedly cited an op-ed by former Senate majority leaders Thomas A. Daschle (D-S.D.) and Robert J. Dole (R-Kan.) published Monday in the Los Angeles Times that said “this is no time to play politics with hunger.”

According to the Census Bureau, almost 14 percent of households in the United States received food stamps in 2012, a total of 16.6 million households. Almost half the recipients, 48 percent, are non-Hispanic whites; 26 percent are black and 21 percent are Hispanics.

The five states with the biggest share of people on food stamps are, in descending order, Mississippi (19 percent) and Kentucky, Maine, Michigan and Tennessee, all at 18 percent. The five states with the smallest share of households getting food stamps are Minnesota and California (each at 9 percent), New Hampshire and North Dakota (each at 8 percent) and Wyoming (7 percent).

Brandishing a cooked steak, bottle of vodka and can of caviar on the House floor, Rep. Jackie Speier (D-Calif.) suggested that money spent by lawmakers on official overseas travel could easily help pay for food stamps. She cited one lawmaker who reportedly received more than $3,500 to spend on food and lodging during a six-day trip to Russia — roughly equal to a year’s worth of SNAP funding for some recipients, she said.

The House bill would cut overall SNAP spending by slightly more than 5 percent over the next decade, largely through two provisions that would significantly affect states.

The first accounts for roughly half the cuts and reinstates limits for many able-bodied, childless adults aged 18 to 50. As a result, 1.7 million people would lose benefits next year, the nonpartisan Congressional Budget Office reported Monday. Under federal law, those able-bodied adults are able to collect only limited benefits — up to three months over a three-year period — unless they work more than 20 hours per week or are in a job-training program.

In recent years, however, as the economic recession grew deeper, the vast majority of states have qualified for waivers on those limits. All but one qualified in fiscal 2011, and 46 states were eligible in fiscal 2012. Forty-four states qualified for fiscal 2013, which ends this month. The House provision would reduce the number of available waivers. Many states with Republican governors, such as Alaska, Arizona, Iowa, Texas and Wisconsin, applied for waivers for all or parts of their states this year.

But not all states will continue to seek the waivers. In a statement earlier this month, Kansas announced that “in an effort to encourage employment over welfare dependency,” it would allow its waiver to expire at the end of the month. The action would drop an estimated 20,000 people from the program. Several states have indicated that they do not plan to seek renewal of their waivers, including Ohio, which announced its stance this month.

But while those states argue that reinstating the work requirements will encourage able-bodied, childless adults to get back to work, critics point to what has been a plodding and uneven recovery in jobs, marked by historically high rates of long-term unemployment.

“Really it’s a punishment for the status of being jobless,” says Ellen Vollinger, legal director at the Food Research and Action Center, a nonprofit advocacy group.

To reduce the burden of figuring out who qualifies for benefits, states are allowed to determine a person’s eligibility for the program based in part on whether they qualify for other low-income benefits. The House measure passed Thursday would restrict that “categorical eligibility,” resulting in $11.6 billion in cuts, according to the CBO.

It may also mean higher costs to figure out who can receive aid. In May, the bipartisan National Conference of State Legislatures argued that a similar proposal would increase administrative costs for already cash-strapped states.

“This limitation in categorical eligibility would increase state administrative costs in SNAP and significantly curtail state flexibility,” the NCSL wrote in the letter. By forcing states to determine eligibility separately, the House bill creates new costs they must bear, the organization argued.