OLYMPIA — Gov. Jay Inslee on Thursday proposed a new capital gains tax to help address a projected state budget gap of more than $2 billion over the next two-year budget cycle.

A state tax on the sale of stocks, bonds and other assets would raise nearly $800 million during the 2015-17 budget period, Inslee said.

Another new tax proposed by the governor this week would raise an additional $380 million for the state’s general fund by charging polluters for carbon emissions. The governor also wants to increase the state cigarette tax by 50 cents a pack, as well as repeal five tax breaks.

Inslee says the state needs new money to answer a state Supreme Court order to better pay for public schools and to address environmental issues.

“It is time to reinvest in our state, and this budget does that,” Inslee told reporters.

The governor’s proposed tax and revenue changes add up to about $1.4 billion and are part of an overall $39 billion operating budget.

Inslee wants to spend most of his budget — $18.2 billion — on public schools. Washington is under court order to increase the amount of money it spends on K-12 education. Social and Health Services would get $6.4 billion, the Health Care Authority would receive $4.4 billion and the state’s colleges and universities would receive $3.4 billion.

The governor wants to levy a 7 percent capital gains tax on earnings from the sale of stocks, bonds and other assets above $25,000 for individuals and $50,000 for those who file jointly. The levy would begin in the second year of the biennium, in January 2016. Inslee says this would affect fewer than 1 percent of families in Washington. Washington’s capital gains tax would be less than similar levies in Idaho, Oregon and California, Inslee said.

Inslee’s spending plan allots $1.6 million for a program to train workers in carbon-composite wing fabrication at the Washington Aerospace Training and Research Center in Everett.

He also wants to put $2.5 million into aerospace and advanced manufacturing apprenticeship programs offered through community colleges and $500,000 into a new aerospace academy for high school graduates.

His proposed capital budget includes $54.6 million for Washington State University to construct a new building in Everett to serve as the future home of the WSU-managed University Center of North Puget Sound.

The four-story, 95,000-square-foot structure would be built in a corner of the parking lot of the College Plaza shopping center, near the corner of North Broadway and Tower Street. If construction begins next year, it could be open in 2017, university officials have said.

But Inslee did not fulfill the request of WSU for $4.5 million to launch additional degree programs at the University Center in Everett, including software engineering, sustainable food systems and aviation maintenance.

The governor’s budget is the first proposal of many expected in the coming months in Olympia. He said he welcomes other ideas that would provide the money needed to boost education spending, satisfy the Supreme Court, protect social services and improve the environment.

“This budget is a start of the conversation, not the finish of one,” Inslee said.

The ranking Republican on the House Appropriations Committee said he looks forward to holding the governor’s ideas up to the bipartisan scrutiny of the legislative process.

“The governor has unveiled some controversial proposals that have given state lawmakers some ideas to think about,” said Rep. Bruce Chandler, R-Granger.

Chandler said an improvement in the state economy is already bringing billions of dollars of new money into the state’s bank account, and that should be enough to balance the budget.

The House’s chief budget writer called the governor’s proposal a good place to begin the discussion on paying for education.

“The governor’s budget will spark a lot of discussion among legislators and interest groups, and that’s what we need to get to a budget that balances and meets the needs of the state,” said Ross Hunter, D-Medina.

The Senate budget writer doesn’t think the governor’s proposal with what he called one of the largest tax increases in state history is a good way to start the conversation.

Sen. Andy Hill, R-Redmond, said he think lawmakers from both parties can come up with a better compromise that still makes children the state’s priority.

“I certainly look forward to working with all parties to fix the problem,” Hill said, noting Democrats and Republicans have been meeting all summer to discuss ideas for education spending.

Jared Kink, president of the Everett Education Association, called the budget “a good start” that leaves the state short of meeting the dictate of the court ruling on school funding and the imperative of voters for smaller classes.

“It’s a good down payment to what the justices and the people want,” said Kink, who drove to Olympia from Everett for the governor’s news conference.

Complying with the demands of Initiative 1351, the class-size measure, will cost an estimated $2 billion in the next biennium, and Inslee’s plan covers less than a quarter of that cost.

“He and the Legislature will need to deal with that,” said Kim Mead, president of the Washington Education Association and an Edmonds resident.

“It’s part of the law now. It does need to be taken care of by the end of this session.”

Said state Rep. Ruth Kagi, D-Seattle, chairwoman of the House Early Learning and Human Services Committee: “The early learning investments are outstanding. They are long overdue.”

“We will have many more children starting school ready to learn,” said Kagi, who represents part of south Snohomish County.

The governor also said a proposed levy on carbon polluters would raise $380 million and a 50-cent per pack tax on cigarettes, along with a separate tax on e-cigarettes and vapor products, would raise an additional $56 million.

Inslee’s plan would also repeal tax breaks on royalties and for oil refineries, limit sales tax exemption to $10,000 on trade-in value of used cars, and impose a tax on the sale of bottled water to consumers.

Inslee said Washington still faces an “enormous budget challenge” because revenues aren’t keeping up with projected expenses, especially in light of the Supreme Court decision mandating more state education spending.

In his 2012 campaign Inslee said he wouldn’t raise taxes. Asked why his proposed budget included tax hikes, the governor said the Legislature had failed to close tax loopholes, and more money was needed to pay for things like education.

“We simply have not been able to generate the revenue necessary,” he said. “I have tried to avoid this route.”

Herald reporter Jerry Cornfield contributed to this story.