(CNN) — One month after the shooting death of Trayvon Martin, nearly three out of four Americans say the police should arrest the neighborhood watch volunteer who pulled the trigger, according to a new national survey.

And the CNN/ORC International poll released Monday also indicates that three-quarters of the public says that neighborhood watch members should not be allowed to carry weapons.

Seventy-three percent of people questioned in the survey say that George Zimmerman should be arrested, with 11% disagreeing and 16% unsure. Zimmerman admits to shooting and killing Martin, an unarmed African-American teenager, in Sanford, Florida, on February 26.

Calls for justice rage on in Trayvon Martin’s killing

Zimmerman, 28, claims Martin attacked him and he shot in self-defense, according to police. Martin’s family and supporters say the unarmed 17-year-old was no more threatening than the bag of Skittles candy and the iced tea he was carrying.

The shooting has grabbed national headlines and has renewed the national conversation about race relations, gun laws, and even how young men dress. It sparked a national furor that reached all the way to the White House, prompting President Barack Obama last week to call for national soul-searching to discover how something so tragic could happen. Protests continue Monday, with rallies planned for major cities across the country.

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Zimmerman is a white Hispanic, and family and supporters of Martin believe race was an issue in the shooting. Zimmerman’s family say he has been mistakenly portrayed as racist.

A special prosecutor is investigating the case, with a grand jury scheduled to begin deliberations on April 10. The prosecutor, Angela Corey, said last week that she does not know if a grand jury will be necessary.

“Nearly two-thirds of whites and 86% of non-whites say Zimmerman should be arrested,” says CNN Polling Director Keating Holland, “as well as majorities of Republicans, Democrats and independent voters.”

Sanford authorities say they could not arrest Zimmerman under Florida’s “stand your ground” law, which allows people to use deadly force to defend themselves anywhere they feel a reasonable fear of death or serious injury. The evidence police had at the time didn’t allow for an arrest, police have said.

Zimmerman’s attorney said Sunday that after reviewing Florida’s “stand your ground” law, he believes it applies to the situation and that his client is innocent.

Shooting renews debate over ‘stand your ground’ laws

Zimmerman said he was driving in his gated community when he saw Martin walking and called 911 to report a suspicious person.

He told the dispatcher he was following the teen, but the dispatcher told him that wasn’t necessary. Moments later, several neighbors called 911 to report a commotion outside, and police arrived to find Martin dead of a gunshot wound.

The survey indicates that 55% of all Americans approve of so-called “stand your ground” laws, although there is a big gender gap on that question, with men approving of the laws 64%-34% and women opposing the measures 52%-46%.

According to the poll, only one in five believe that neighborhood watch members should carry guns, with 76% saying they should not be allowed to be armed.

The CNN poll was conducted by ORC International on Saturday and Sunday, with 1,014 adults nationwide questioned by telephone. The survey’s overall sampling error is plus or minus three percentage points.