Boxes of petitions for Initiative 594 are seen at the secretary of state’s office Wednesday, Oct. 9, 2013, in Olympia, Wash. (AP photo/Elaine Thompson)

Voters in Washington state appear poised to approve more background checks on firearms purchases at gun shows and in private sales, according to a new survey.

The poll, conducted by the University of Washington for Seattle’s public television channel KCTS, shows Initiative 594 earning 64 percent of the vote, including leaners. Just 31 percent say they will vote or are leaning toward voting against the measure.

Initiative 594 would mandate background checks on everyone purchasing a firearm in Washington. It exempts antiques and gun transfers between immediate family members, but it requires gun dealers to receive confirmation in writing that a buyer has checked.

Supporters have spent far more than opponents of the proposed measure, thanks to big contributions from billionaires, such as Bill Gates, Steve Ballmer and Nick Hanauer. The primary committee supporting the measure has raised more than $10 million, compared with just over $600,000 raised and spent by the National Rifle Association and Washington Citizens Against Regulatory Excess, the two primary opponents.

Other surveys have showed the measure passing by wide margins, too. An Elway Poll conducted two weeks ago showed 60 percent supporting the measure.

It’s not clear whether last week’s shooting at a high school in Marysville, north of Seattle, has had any impact on the case. Officials have said the shooter used a .40-caliber Beretta handgun that was legally purchased and registered to a relative.

A rival initiative backed by gun-rights advocates is winning by a narrow plurality, 45 percent to 43 percent, according to the UW poll. That measure, Initiative 591, would prevent Washington from implementing background checks that are stricter than those implemented by the federal government. The Elway poll showed I-591 at just 39 percent support.

Gun-rights supporters began collecting signatures for their initiative in hopes of stopping the stricter law. But that approach opened a schism in the gun-rights community: While the Second Amendment Foundation, based near Seattle, has worked to pass I-591, the National Rifle Association has kept its focus on defeating I-594, rather than advocating for I-591.

If both measures pass, the state would face its first-ever instance of conflicting ballot initiatives. There is no statute or court precedent to account for conflicting voter-approved laws in Washington, meaning the state Supreme Court would likely have been forced to weigh in.