Gov. Kathy Hochul on Tuesday unveiled a $233 billion budget for New York State that includes $2.4 billion to help New York City manage its migrant crisis — a $500 million increase reflecting the mounting costs as immigrants continue to arrive.

The budget proposal sought to thread the needle between the necessity to exert financial discipline as projected multibillion-dollar deficits loom, and the pressing needs posed by the migrant situation as well as substantial increases in Medicaid costs.

The presentation built on the State of the State address that Ms. Hochul gave last week, in which she outlined a broad vision for bolstering mental health care and public safety across the state, but spoke only briefly about the migrant crisis.

The issue took center stage on Tuesday, with the governor offering a package that will help cover the costs of sheltering migrants and asylum seekers, as well as provide funds for case management, National Guard staffing, medical and legal bills, and employment-related services.