The administration would drastically change the way states are allocated funding for programs that support disadvantaged K-12 students. The budget proposes consolidating 29 programs into a $19.4 billion block grant that would dispense funding to states, who would then determine how to use it. Among the programs that would be zeroed out to fund the grant are 21st Century Community Learning Centers, which funds after-school programs for low-income students; funding for programs in rural schools and magnet schools; and funding for homeless and migrant students.

The measure would overhaul the role of the Education Department, reducing its staff and administrative costs, and “empower states and districts to decide how to best use federal funds to meet the needs of their students,” the department’s budget said.

The budget also proposes creating an entirely new agency to police tobacco, moving that responsibility out of the Food and Drug Administration and into the Department of Health and Human Services.

The proposal is also notable for what it did not include. In previous years, Mr. Trump’s budget has proposed repealing the Affordable Care Act and replacing it with a system that would provide block grants of funding to states with far fewer rules about how the money should be spent. The new budget backs away from that approach. It leaves the law’s funding in place but asks Congress to develop policies that would “advance the president’s health reform vision,” with a corresponding price tag, which it says would save $844 billion over the decade.

The budget’s approach to health care is particularly striking given the administration’s actions in court. The White House has joined a lawsuit brought by a group of Republican states that would seek to invalidate all of the Affordable Care Act. The Supreme Court is deciding whether it will take up that case or allow the lower courts to continue reviewing it. The president has repeatedly promised to release a health care plan that could be deployed if he wins in court, but has yet to do so.

It still makes major changes to health care programs, including several that would tend to lower federal spending on Medicaid, by reducing the share of medical bills the federal government will pay for the Obamacare expansion population and imposing new requirements on beneficiaries who wish to enroll. All together, it proposed combined cuts to spending in Medicaid and Affordable Care Act subsidies that equal a trillion dollars — cuts that would mean substantial program changes.

Democratic candidates, in contrast, have offered detailed plans, which typically cost trillions of dollars raised via new taxes on corporations and the rich, to expand health care coverage and reduce costs for American patients. Health care remains a top issue for many of Mr. Trump’s supporters, while Democrats’ “Medicare for all” plans have fared well in many opinion polls.