The budget also requests $700 million for school safety initiatives being coordinated by several agencies, including $200 million for the Education Department. The funding would help schools finance emergency operation plans, counseling and behavioral health programs. There are no requirements for firearms, the department said. A $1 billion federal grant program that school districts looked to tap last year for firearms would be eliminated.

A few domestic spending programs would see increases, if Mr. Trump’s budget were to become law. Those include efforts to reduce opioid addiction, as well as a 10 percent increase in health care spending for veterans. Mr. Trump will also propose a new voucher program for education, $200 billion in infrastructure spending and efforts to reduce the cost of prescription drugs.

The budget would not balance for 15 years, breaking Mr. Trump’s 2016 campaign promise to pay off the entire national debt within eight years. Mr. Trump’s first budget proposed balancing revenue and spending in 10 years. The budget released on Monday forecasts trillion-dollar deficits for four straight years, starting in 2019. Those are largely the result of Mr. Trump’s tax cut, which has been financed through increased government borrowing.

Budget details released by White House officials highlight several areas of conflict between Democrats and Mr. Trump, starting with immigration enforcement. Along with renewing the wall funding fight that led to a record government shutdown late last year, Mr. Trump is asking for more personnel at Customs and Border Protection and Immigration and Customs Enforcement and for a policy change meant to end so-called sanctuary cities, which do not hand over undocumented immigrants to federal officials when they are arrested in local crimes.

“This budget is a recipe for American decline,” said Representative John Yarmuth, Democrat of Kentucky and the chairman of the House Budget Committee. “It’s laughable that this budget is subtitled ‘Promises Kept,’ because in fact there are a lot of promises that have been violated in this budget.”

“This is a budget that we will not take seriously when we are working on our budget and spending priorities for 2020,” he said.

Disapproval from Democratic presidential candidates was just as blunt. “This is a budget for the military industrial complex, for corporate C.E.O.s, for Wall Street and for the billionaire class,” Senator Bernie Sanders, independent of Vermont, said in a statement. “It is dead on arrival.”