Education spending also would increase by almost $700 million.
The governor has already vetoed five pieces of legislation, including the two-year state budget on Tuesday.
"Simply put, this budget short changes our state at a time when it doesn't have to".
"It sets out collaborative steps and key solutions that we can take to stem the crisis", Gov. Cooper said.
Last week, Senate and House leaders unveiled details of the spending plan and urged Cooper to sign the measure, but the Democratic governor's office has signaled that a veto could be on the horizon, with the governor calling the budget "fiscally irresponsible".
Governor Roy Cooper announced Tuesday that "North Carolina's Opioid Action Plan", to combat the opioid epidemic.
"The legislative budget includes no money to help teachers buy school supplies, nothing for schools to hire additional support personnel, and drains millions of dollars from public education to pay for private school vouchers with no accountability", said a press release from the governor's office.
The state needs to honor that growth and "enable the big dreams" of the state's people, Cooper said.
Cooper has blasted the budget as "irresponsible" since the compromise bill was released last week, but his veto arrived almost 24 hours after he said Monday he would veto the budget "today".
The $23 billion budget would give teachers an average pay raise of 3.3 percent - weighted toward experienced teachers - in the coming year, and would raise most other state employees' pay by a flat $1,000. "What we need to get our leaders across the state and across our country to see is that investment in health care is a critical component of this", Cooper said. Cooper sought at least 10 percent. The House, also dominated by Republicans, is expected to vote to override on Wednesday, passing the budget bill into law. Instead, Republicans invest money in expanding a growing array of bonuses for teachers based on student performance or increased responsibilities.
Republicans contend the budget contains several items that Cooper sought, including tax reductions that benefit low- and middle-income families and efforts to address opioid abuse.
RALEIGH, N.C. (AP/WNCN) - Debate and votes will be plentiful all week at the North Carolina General Assembly as Republican legislators aim to adjourn their annual work session before the July 4 holiday.
"This budget neglects our schools and our economy at a time when North Carolina should be making public education stronger, not giving special breaks to those at the top", Cooper wrote.