More than half of Americans want stricter gun laws, while still preserving the rights of most people in most places to carry most types of guns, a Pew Research Center survey has found.

While half of Americans see gun violence as a very big problem in their country, fewer than 10% of American adults said that “almost no one” should be able to legally own a gun, and only 10% said that “almost no types” of guns should be legally available to buy. Overall, however, 52% want stricter gun laws.

In other countries, last week’s mass shooting on members of Congress that left House majority whip Steve Scalise seriously wounded might have started a debate over stricter gun control laws. In America, the response was different: the leading gun rights organization agreed to train members of Congress and their staff on how to use guns in self-defense.

The National Rifle Association announced on Wednesday that it had agreed to offer firearms training courses to members of Congress “regardless of political affiliation”. But the new survey suggests that there are stark partisan differences in how Democratic and Republican gun owners use their firearms – as well as in their openness to new gun laws.

The Pew survey of nearly 4,000 American adults found some areas of agreement. Strong majorities of gun owners and non-gun owners support background checks for private sales and sales at gun shows, as well as barring those on terror watchlists from buying guns – two federal policies Republicans in Congress have rejected.

Even among gun owners, though, the survey found clear differences in firearm usage. Republican gun owners reported shooting or going to a gun range more often than Democratic gun owners did. And 55% of Democrats who reported owning a handgun said they never carry their gun with them. By contrast, the majority of Republican gun owners said they carry their handgun with them at least part of the time.

About 25% of Democrats reported owning a gun or living in a household with a gun, compared with 57% of Republicans.

Views on what guns mean, and what gun laws the country needs, were also markedly different based on party affiliation. Nine out of 10 Republican gun owners said the right to own firearms is essential to their sense of freedom, compared with only four in 10 Democratic gun owners.

More than 80% of gun owners who are Republican or lean Republican support allowing teachers or officials to carry guns in primary and secondary schools, compared with only 42% of Democratic and Democratic-leaning gun owners.

Two-thirds of Democratic and Democratic-leaning gun owners support banning assault-style weapons and high-capacity magazines, compared with only about one-third of Republican and Republican-leaning gun owners.

Nearly half of Republican and Republican-leaning gun owners support allowing people to carry concealed guns without a permit, while 85% of Democratic and Democratic-leaning gun owners oppose this.

There is a larger partisan gap between Democrats and Republicans on views of the NRA than there is between gun owners and non-gun owners.

The survey suggested Americans’ relationship with guns is entrenched: most gun owners cannot imagine ever not owning a gun, and even the majority of those who don’t currently own a gun say they could see themselves owning a gun in the future. More than 70% of Americans say they have fired a gun at some point in their lives. And more than 90% see guns as playing some role in American culture.

While they express strong support for gun ownership among at least some people, and gun carrying in at least some places, a large number of Americans have seen those around them directly affected by gun violence.

About a quarter of Americans said they or their families have been threatened or intimidated with a gun. More than 40% of Americans say they personally know someone who has been shot, whether intentionally or accidentally. Among black adults, the proportion rises to 57%.

By contrast, only 17% of current gun owners – and 7% of Americans overall – said they had personally used a gun to defend themselves, their families, or their property.

The new Pew survey found a slightly higher percentage of Americans who said they own guns – about 30% – than some other estimates.

But the survey found similar overall demographic trends in gun ownership, with about half of white men saying they owned a gun, compared with about a quarter of white women and non-white men, and 16% of non-white women.

The NRA has strong support among gun owners overall, but a sizable minority of gun owners expressed disapproval of the NRA’s political power. Nearly one in three gun owners said the group has too much power over American gun laws. Half of Americans who are not gun owners agreed.

NRA spokeswoman Jennifer Baker said she did not immediately have more details on the firearms training sessions for members of Congress.