The share of Americans in poverty, as measured by the Census Bureau, has fallen every year since 2012, an improvement that is historically correlated with declining food-stamp participation. Enrollment in the program began to decline in 2014 and 2015, by about 2 percent, and in Mr. Obama’s final year in office by more than 3 percent. In Mr. Trump’s first three years, that trend has accelerated, from a 4.5 percent drop in 2017 to a nearly 7 percent drop last year.

Improving employment opportunities and pay increases have made millions of workers ineligible for food stamps because they now earn too much money. Wage growth is accelerating for the lowest-paid workers in the economy, and the share of the population working or looking for work is rising.

Mr. Trump has also taken steps to restrict eligibility for safety-net benefits, like allowing states to add work requirements to Medicaid and threatening to deny citizenship to legal immigrants who enroll in public assistance.

The Department of Agriculture has proposed three rules that tighten eligibility and work requirements for food stamps. One of those proposals will go into effect in April, making it more difficult for states to waive certain work requirements. The department estimates that more than 700,000 people could lose their food assistance because of the rule.

The other two rules are still pending, but if all three had taken effect in 2018, more than three million people would have lost their food assistance, an analysis by the Urban Institute found.

“A commitment to the transformative power of work is why I signed an Executive Order instructing agencies to reduce dependence on welfare programs by encouraging work,” Mr. Trump wrote in the introduction to the annual Economic Report of the President, to be released on Thursday.

Mr. Trump has also taken credit for the declines in the number of Americans taking benefits from programs his administration collectively calls “welfare,” including Medicaid, the Children’s Health Insurance Program and Temporary Assistance for Needy Families, which provide health coverage and cash assistance to low-income families.