CONCORD, N.H. — State revenues are 2 percent above target halfway through the fiscal year, but Democratic Gov. Maggie Hassan announced new actions Tuesday to avoid a possible budget deficit.

Revenues through December were $19 million above target, according to figures released by the administration. Business revenues have been consistently below target but performed stronger in December than previous months. Higher revenues from meals and rooms, insurance and real estate taxes have offset the low business tax revenues to keep the state ahead of its target.

Democratic lawmakers say continually underperforming business revenues could lead the state toward a shortfall, while Republicans say overspending is the root problem. There is a potential for a shortfall in the state’s $10.7 billion, two-year budget that ends June 30 but Hassan hasn’t said how much the deficit could be.

Hassan had already ordered state agencies to cut $18 million from their current budgets to head off a shortfall and announced further actions Tuesday.

She proposed $1.4 million in cuts to the legislative and judicial branches and the Fish and Game Department. Her plan also seeks to take $1.7 million from the Health Care Reserve Fund that provides health insurance for state employees. All those actions would require legislative approval.

Beyond the cuts, Hassan proposed a tax amnesty program that would reduce penalties and fees on people who have fallen behind on their taxes. Previous tax amnesty programs in 1998 and 2002 generated $13.5 million and $14.9 million, respectively, in new revenue.

Hassan’s office said she will present a budget reduction plan for the Department of Health and Human Services this month. The department, the state’s largest, is already running $48 million over budget.

Hassan will present her proposed budget for the next two years in February.