(Reuters) - More than 80 percent of Americans want to limit firearms access for people with mental illness and require background checks at gun shows and in private sales, according to a Pew Research Center survey released on Thursday. Eighty-three percent also favor barring gun purchases by those on federal no-fly or watch lists, the survey found. But gun owners were far less supportive than non-owners of creating a federal database to track gun sales or to ban assault-style weapons and high-capacity magazines. The survey of 3,930 U.S. adults, including 1,269 gun owners, in March and April, provided a snapshot of American views on guns and gun policies as the nation grapples with gun violence. On June 14, an Illinois man opened fire on Republican members of Congress with legally purchased guns during a baseball practice near Washington, wounding Louisiana Representative Steve Scalise.  A few hours later, a UPS driver opened fire with a handgun inside a United Parcel Service Inc delivery center in San Francisco, killing three co-workers before fatally shooting himself. Some advocates called for a renewed push for gun control measures, as the Republican-controlled Congress has sought to relax existing gun laws. The National Rifle Association has opposed expanded background checks and argued the government was already being notified when someone on a no-fly list attempts to buy a gun. Pew’s survey respondents often diverged based on whether they were gun owners or non-owners, Republicans or Democrats and urban or rural residents. “Overall, 52 percent of Americans say gun laws should be stricter than they are today,” according to Washington-based Pew. Forty-four 44 percent of adults surveyed said they personally knew someone who was shot, accidentally or on purpose, and 83 percent believed gun violence was a very big or moderately big U.S. problem. As for violence in their local communities, 49 percent of black respondents said it was a very big problem, compared with 11 percent of whites.  A large majority said easy access to illegal guns contributed to gun violence, but just as many thought expanding gun ownership would boost crime as reduce it. Among all adults, 89 percent favored policies preventing the mentally ill from purchasing guns, and 84 percent favored background checks in private sales and at gun shows.  Tracking gun sales was favored by 71 percent overall, banning assault weapons by 68 percent, and banning high-capacity magazines by 65 percent, with gun-owners showing less approval than non-owners. 