Terry Eyler walks around looking at handguns as thousands of customers and hundreds of dealers sell, show and buy guns and other items during the Nation's Gun Show at the Dulles Expo Center in Chantilly, Va., on Oct. 3. (Jabin Botsford/The Washington Post)

As Democrats look to make gun violence a core issue in the 2016 presidential campaign, a new Washington Post-ABC News poll finds wide agreement that gun violence is a problem but bitter and stark division on whether new gun laws should trump the constitutional right to gun ownership.

The survey finds that 46 percent say new laws to reduce gun violence should be a bigger priority, while 47 percent say it's more important to protect the right to own firearms. This marks a shift away from gun laws since April 2013, when Democrats' push for increased background checks fell short in the aftermath of the massacre at an elementary school in Newtown, Conn.; back then, a 52 percent majority said new laws should be a priority.

Republicans and Americans in rural areas account for the shift toward giving gun rights higher priority. Since 2013, the number of rural Americans who prioritize gun rights over new laws has grown from 46 percent to 61 percent, and the share of Republicans has jumped from 58 percent to 71 percent.

Here's what you need to know about the prevalence of what the FBI calls "active shooter incidents" in the U.S. (Osman Malik and Sarah Parnass/The Washington Post)

The public's mixed views on gun laws — despite continued overwhelming support for expanding background checks and other specific policies — have vexed policymakers on an issue that the vast majority regard as a national problem. Fully 82 percent say gun violence is a serious problem in the United States, and 58 percent call it a "very serious" problem.

Regular mass shootings have brought the issue repeatedly to the nation's front pages. As of Oct. 1, 294 mass shootings have occurred in 2015 (defined as an incident where four or more people are killed or injured by gunfire).

But while many have called for stricter gun laws in their wake, the Post-ABC poll finds far more point to problems treating people with mental health issues. By a more than 2-to-1 margin, more people say mass shootings reflect problems identifying and treating people with mental health problems rather than inadequate gun control laws (63 percent to 23 percent).

There are wide partisan divisions on this issue; 82 percent of Republicans say shootings reflect a failure to identify and treat people with mental health problems, compared with 65 percent of independents and 46 percent of Democrats.

Americans have strong opinions about overall priorities in the gun debate, with big divisions by partisanship, between cities and rural areas, and between men and women.

Nearly 8 in 10 feel "strongly" about whether new laws should be enacted to prevent gun violence (38 percent) or that gun rights should take precedence (40 percent). Seven in 10 Democrats prioritize new gun laws, while an almost identical number of Republicans say gun rights matter more. Six in 10 Democrats and Republicans line up "strongly" on one side or another.

Just more than half of people living in urban areas -- 52 percent -- say new gun laws are a bigger priority than protecting gun rights. That dips to 45 percent in suburban areas and to 33 percent among those in rural parts of the country. Women are 13 percentage points more likely to prioritize new gun laws than men, 52 percent to 39 percent.

The Post-ABC poll was conducted Oct. 15-18 among a random national sample of 1,001 adults, including land-line and cellphone respondents. Full results have a margin of sampling error of plus or minus 3.5 percentage points.