OLYMPIA — Washington Gov. Jay Inslee proposed a tax on fossil fuels Tuesday that his administration estimates would initially raise gasoline prices by 18 cents a gallon, with annual increases to follow.

The cost of electricity would go up by about 5 percent and natural gas by roughly 10 percent, according to Inslee advisers. Administration officials say they hope that motorists, households and businesses will respond to rising energy prices by burning less fossil fuel.

In his state of the state address Tuesday, Inslee promoted the carbon tax as a response to climate change.

“I believe Washingtonians will be together on this issue,” he said. “On this, there is no geographic divide in our state. The Eastern Washington farmer whose irrigation supply is threatened by low snowpack faces the same crisis as the Western Washington shellfish grower whose baby oysters are threatened by ocean acidification caused by carbon pollution.”

Inslee, a Democrat, has made climate change his signature issue. He has previously proposed taxing carbon emissions, but a tax has not passed the Legislature. Democrats hold slight majorities in the House and Senate and will need to either unanimously support a tax or find Republican votes.

In the official Republican response to Inslee’s address, Kennewick Sen. Sharon Brown said the tax would burden families and stifle businesses. “That would be a move in the wrong direction, resulting in opposition from both parties,” she said.

Inslee proposed a $20-per-ton tax on greenhouse gases emitted by energy generators and transportation fuel suppliers. The tax would increase, indefinitely, by 3.5 percent plus inflation each year. The administration estimates the tax would generate $1.5 billion in the first two years.

Initially, under Inslee’s proposal, the money would replenish a reserve fund that the governor wants to tap to pay state Supreme Court-ordered pay raises for public school employees.

Inslee proposed that in the future half the money go for programs to help the state cut carbon emissions by 80 percent from 1990 levels by 2050.

Some 35 percent of taxes would be set aside for projects such as thinning forests, preventing floods and irrigating farmland. The Department of Commerce would handle the remaining 15 percent and come up with a plan to help poor people and workers hurt by the tax.

The legislation carves out exemptions from the tax, including one for fuel used by farmers. Senior policy adviser Reed Schuler said the administration wants to protect the state’s agricultural industry.

He said the administration has not figured out the details on how to shield farmers from higher energy costs.

The Inslee administration does not make any claims that the policy would affect the climate, though it would align Washington with carbon-reduction efforts throughout the world.

Inslee urged lawmakers to pass the tax before adjourning in March.

“We have just 59 days to do our part to save our children from a certain endless cycle of crop-killing droughts one year and rivers spilling their banks the next. To save salmon from dying in ever-warming rivers and our forests from being reduced to plumes of ash,” Inslee said.

Republican leaders said the carbon tax would hit low- and middle-income residents. “For most of us, this is about a tax increase and controlling people,” said Rep. David Taylor, R-Moxee.

Senate Minority Leader Mark Schoesler, a Ritzville Republican, said people who cut their energy consumption couldn’t triumph against an ever-escalating carbon tax.

“You cannot win,” he said. “It keeps going up.”