BATON ROUGE, La. — Facing a $1.6 billion shortfall and an entrenched structural deficit, officials from the administration of Gov. Bobby Jindal of Louisiana introduced a 2016 budget proposal on Friday with deep cuts but also some unexpected flexibility on taxes.

The proposed cuts are substantial, coming after years of routine and severe reductions. They would potentially result in the closures of community health care clinics and historic sites. Hospitals partly privatized by Mr. Jindal would get $142 million less than they had sought. Spending on higher education would be lower by $141 million, a further 6 percent reduction after years of cuts.

But officials said the plan would avoid some of the worst-case situations by reworking certain tax credits in a way that would make an additional $526 million available to meet current expenses. This came as a surprise to many, given that Mr. Jindal, a Republican who is widely assumed to be running for president, has been so firm in his opposition to new taxes that even the renewal of taxes already in place has been off limits.

Jindal administration officials insisted that the proposed changes did not constitute a tax increase, because they would simply take some refundable tax credits and turn them into nonrefundable tax credits. “Our guardrails are very clear,” said Kristy H. Nichols, the state’s commissioner of administration, who presented the budget to a legislative committee. “We won’t raise taxes without an offset or a credit.”