 -- Americans overwhelmingly support barring gun purchases by individuals on the FBI’s terrorist watch list — an initiative that has thus far failed in Congress. And Hillary Clinton has moved ahead of Donald Trump in trust to handle terrorism, boosted by her response to the Orlando attack.

Eighty-six percent of respondents in an ABC News/Washington Post poll released today favored a ban on gun purchases by those on the watch list. The survey also found an increase in support for an assault weapons ban, to 51 percent, even as most Americans were in favor of encouraging more people to carry guns legally for self-defense. With broad worries about other lone-wolf attacks, most favored increased surveillance of suspected terrorists, even if that intrudes on privacy rights.

See PDF for full results and charts.

Mirroring her rebound in the race for the White House, Clinton led Trump, 50 percent to 39 percent, in trust to handle terrorism in this poll, produced for ABC by Langer Research Associates. That’s similar to the gap in March, after a more closely divided view last month.

This reflected Clinton’s superior marks for her response to the shooting in Orlando. More respondents thought she did a better job than Trump in responding to the attack overall (46 percent to 28 percent) and showed better temperament in her response (59 percent to 25 percent). More said Clinton gave them confidence that she could handle a similar incident as president (53 percent to 34 percent). She also prevailed, albeit more narrowly, in having better proposals for preventing attacks (44 percent to 35 percent).

Clinton’s biggest gains in overall trust to handle terrorism came among some key groups, including those who preferred Bernie Sanders for the Democratic presidential nomination, white men and white Catholics, as well as among Democrats in general. Trump lost ground in most of these groups, as well as (slightly) among men overall, those without a college degree and liberals.

Anxiety was substantial; 86 percent of those polled said they were concerned about other lone-wolf attacks, including a majority, 53 percent, who were very concerned. There was continued skepticism that the government can prevent these incidents; two-thirds of respondents said they had little or no such confidence. That was down 10 percentage points from its level after the Dec. 2 attack in San Bernardino, California, but is still high.

Fifty percent of respondents approved of the way President Barack Obama has handled the threat of terrorism, versus 45 percent who disapproved — the best he has done on this issue since January 2014. That accompanies a more general improvement in his approval rating this month.

Policies

Support varied for policy proposals to address the issue. Most divisive was the idea of nationwide ban on the sale of assault weapons (51 percent support, 48 percent oppose), with most on both sides feeling strongly about their position. That said, support for an assault weapons ban was up 6 points from its more-than-20-year low in December — the sole ABC/Post survey to date to find majority opposition to an assault weapons ban.

The biggest increases in support were among Northeasterners (up 12 points, to 65 percent), middle- to upper-income adults (up 12 points, to 49 percent), Democrats and Democratic-leaning independents (up 11 points, to 69 percent), moderates (up 11 points, to 57 percent) and nonwhites (up 10 points, to 59 percent). There was a 20-point increase among strong conservatives, to 35 percent support overall.

In sharp contrast with views on assault weapons, there was wide agreement on trying to keep guns out of the hands of those on the FBI’s list of people with possible connections to terrorism. The 86 percent support for this proposal is similar to the level of support in past ABC/Post polls for expanded background checks on people buying guns at gun shows or online.

Additionally, 72 percent supported increasing surveillance of people suspected of links to terrorism, even if it intrudes on privacy rights. That followed a historical pattern of willingness to forgo privacy for safety when it comes to countering the threat of terrorism.

In another result, more respondents supported than opposed encouraging more people to carry guns legally for use in self-defense, 54 to 42 percent. Not surprisingly, 76 percent of those who opposed an assault weapons ban supported more people legally carrying guns, while 61 percent of those who backed a ban opposed encouraging carrying guns for self-defense.

Islam

Trump proposed temporarily barring Muslims who are not U.S. citizens from entering the United States. In exit polls, majorities of Republican primary voters supported this idea. By contrast, among all Americans, 52 percent opposed temporarily barring Muslims, and 43 percent supported it.

At the same time, more respondents agreed than disagreed with GOP criticism of Obama for his unwillingness to use the term “radical Islam.” Forty-eight percent said they thought “leaders should say terror attacks are caused by radical Islam because this accurately identifies the cause,” while 40 percent said “leaders should not use the phrase radical Islam because it lends legitimacy to terrorists by falsely suggesting that their actions are supported by Islamic teachings.”

Support for using the term “radical Islam” peaked among Republicans and strong conservatives; it was also high among men, whites, older adults and those who are better off financially. Support for temporarily barring non-U.S. Muslims also peaked among Republicans and strong conservatives, especially among Republicans and GOP-leaning independents who favored Trump for the nomination. Seventy-eight percent in this group favored a ban, versus 55 percent of Republican-leaning respondents who preferred someone else for the party’s nomination.

Methodology

This ABC News/Washington Post poll was conducted by landline and cellular telephone June 20 to 23, 2016, in English and Spanish, among a random national sample of 1,001 adults. Results for the full sample have a margin of sampling error of 3.5 points, including the design effect.

The survey was produced for ABC News by Langer Research Associates of New York City, with sampling, data collection and tabulation by Abt-SRBI of New York City. See details on the survey’s methodology here.