Americans overwhelmingly support the nationwide protests that have taken place since the killing of George Floyd at the hands of police in Minneapolis, and they say police forces have not done enough to ensure that blacks are treated equally to whites, according to a Washington Post-Schar School poll.

President Trump receives negative marks for his handling of the protests, with 61 percent saying they disapprove and 35 percent saying they approve. Much of the opposition to Trump is vehement, as 47 percent of Americans say they strongly disapprove of the way the president has responded to the protests.

The poll highlights how attitudes about police treatment of black Americans are changing dramatically. More than 2 in 3 Americans (69 percent) say the killing of Floyd represents a broader problem within law enforcement, compared with fewer than 1 in 3 (29 percent) who say the Minneapolis killing is an isolated incident.

That finding marks a significant shift when compared with the reactions in 2014 to police killings of unarmed black men in Ferguson, Mo., and New York. Six years ago, 43 percent described those deaths as indicative of broader problems in policing while 51 percent saw them as isolated incidents.

Overall, 74 percent of Americans say they support the protests that have been carried out in cities and towns across the country since the May 25 killing of Floyd, which occurred after police held him on the ground and one officer pressed his knee to the victim’s neck for nearly nine minutes. “I can’t breathe,” Floyd said as he died.

The recent demonstrations have bipartisan appeal, with 87 percent of Democrats saying they support them, along with 76 percent of independents. Among Republicans, the majority — 53 percent — also back the protests.

The widespread support for the protests comes amid mixed views of whether those events have been mostly peaceful or mostly violent. On that question, Americans are evenly divided, with 43 percent saying the protests have been mostly peaceful and an identical percentage describing them as mostly violent. Thirteen percent say the protests have been equally peaceful and violent.

Views on this split along ideological and partisan lines: Most liberals (70 percent) and Democrats (56 percent) say the protests were mostly peaceful, while most conservatives (60 percent) and Republicans (65 percent) say they were largely violent. Independents are split similarly to the country overall, with 44 percent saying the protests were mostly peaceful, 42 percent mostly violent.

But support for the protests is evident regardless of whether they are seen as mostly violent or mainly peaceful.

Strikingly, among those who say the protests were mostly violent, 53 percent support the nationwide demonstrations while 46 percent oppose them. Among those who said protests have been largely peaceful, 91 percent support them.

Neither protesters nor police come in for significant criticism for the violence, as Americans appear to be taking a nuanced view that separates those participants from others doing damage. When people were asked whom they blame the most when violence has occurred, 10 percent say protesters, 14 percent say police, and 66 percent blame “other people acting irresponsibly.”

The survey also asked about the use of force by police in dealing with the protests. Half of all Americans (50 percent) say police have been handling demonstrations by peaceful protesters “about right,” while 44 percent say law enforcement personnel have used too much force.

When asked about people who have been looting or vandalizing businesses, 47 percent say police have not used enough force against them, 34 percent say police have handled it about right, and 16 percent say too much force was used.

Casting ahead to the November election, which pits Trump against former vice president Joe Biden, half of all Americans (50 percent) say they prefer a president who can address the nation’s racial divisions, compared with 37 percent who say they want a president who can restore security by enforcing the law. While the poll did not measure presidential preference, Biden has campaigned as best suited to unite the country’s racial divisions, while Trump has cast himself as best to restore security, repeatedly tweeting “LAW AND ORDER!” in recent days.

Floyd’s killing is one of a string of such incidents over the years resulting from confrontations between local law enforcement officers and unarmed African Americans, most of them men. On the question of whether police have done enough to address issues of inequitable treatment of blacks and whites, 81 percent said police need to continue to make changes to assure equal treatment of whites and blacks, with 13 percent saying they have made the needed changes.

On this question, clear majorities across political and demographic groups say police need to do more, with the smallest majorities among those identifying as “very conservative” (59 percent), Republicans (66 percent) and those with incomes of $100,000 or more (72 percent). All other groups expressed even higher levels of support in saying more action is needed by police to achieve equal treatment.

The results of the new Post-Schar School poll, when compared with a Post-ABC News survey from December 2014, highlight the dramatic shifts in attitudes about police violence against black Americans among virtually every demographic and political group.

Currently, 86 percent of Democrats, 69 percent of independents and 47 percent of Republicans say the Floyd killing represents a broader problem rather than an isolated incident. More than 2 in 3 whites and 3 in 4 nonwhites say the same. (The number of blacks in the survey was too small to measure independently.)

Overall, since 2014, that represents a 26-point shift in favor of the perception that the killings represent broader problems, a change that is replicated among demographic groups. Among both Republicans and independents, the shift is 28 points, while among Democrats it is 21 points. The biggest changes are among whites overall (a 33-point shift) and white women (38 points).

“The president is way on the wrong side of the growing national consensus that evidences a big shift in attitudes among whites, including Republicans,” said Mark Rozell, dean of the Schar School. “Even the GOP consensus is splintering.”

The view that Floyd’s killing was not an isolated incident is shared by majorities across all demographic groups.

But some groups are more likely to say that than others. Women are 10 points more likely than men to say it represents a broader problem, and whites with college degrees are 10 points more likely than whites without college degrees to say so.

Three-quarters of those under 50 say the killing is a sign of a broader problem, compared with just over 6 in 10 of those 50 and older. And while about 7 in 10 white people under 65 say Floyd’s killing is a sign of a broader problem, that drops to less than 6 in 10 among white people 65 and older.

Republicans generally agree with views of the protests expressed by Trump. Last week he called himself “your president of law and order and an ally of all peaceful protesters” in a Rose Garden statement, made as police and military troops forcibly cleared a demonstration near the White House. He also said the country was in the grip of “professional anarchists, violent mobs, arsonists, looters, criminals, rioters, antifa and others.” He told mayors and governors that they needed to dominate the streets to restore order.

More than 7 in 10 Republicans approve of Trump’s handling of the protests, a view shared by just over one-third (35 percent) of the overall population. Republicans also have a more negative view of the protests; while 43 percent of the public says the protests have been “mostly violent,” 65 percent of Republicans hold this view.

Almost half of all Americans (47 percent) say police have not used enough force in responding to episodes of looting and vandalism, a figure that rises to 72 percent among Republicans. And 63 percent of Republicans say they prefer a president who would restore security, when 50 percent of the overall population instead prefers someone who could deal with the country’s racial divisions.

The poll was conducted by The Washington Post and the Schar School of Policy and Government at George Mason University. It was administered by telephone June 2-7 among a random national sample of 1,006 adults, 70 percent of whom were reached on cellphones and 30 percent on landlines. The margin of sampling error is plus or minus 3.5 percentage points; the error margin is larger for results among subgroups.

Emily Guskin contributed to this report.