Republican presidential candidate Herman Cain said Saturday that part of his immigration policy would be to build an electrified fence on the country’s border with Mexico that could kill people trying to enter the country illegally.

The remarks, which came at two campaign rallies in Tennessee as part of a barnstorming bus tour across the state, drew loud cheers from crowds of several hundred people at each rally. At the second stop, in Harriman, Tenn., Mr. Cain added that he also would consider using military troops “with real guns and real bullets” on the border to stop illegal immigration.

The remarks were among the most pointed yet by Mr. Cain about illegal immigration, and they come as he is enjoying a surge in national political polls on the back of his victory in a recent Florida straw poll. They also follow on remarks made by Representative Michele Bachmann on Saturday during a speech on illegal immigration in Iowa, in which she also advocated a border fence.

It is not the first time that Mr. Cain has floated the idea of an electrified fence. He has told the story many times of a caller to his former radio show who chastised him for talking about building a border fence, saying that such an idea was impractical. Mr. Cain often says he told the caller that he had recently returned from China, and if the Chinese could build the Great Wall then America could build a border fence.

Last summer, after President Obama remarked that some Republicans seemed to want a moat filled with alligators in addition to a fence, Mr. Cain responded by saying that he would indeed add an alligator-filled moat to his proposed fence, which would be topped with electrified barbed wire.

In his remarks on Saturday, Mr. Cain appeared to go a step further. Speaking to a rally sponsored by the Roane County Tea Party, Mr. Cain said that part of his plan would be to “secure the border for real” with a fence.

“It’s going to be 20 feet high. It’s going to have barbed wire on the top. It’s going to be electrified. And there’s going to be a sign on the other side saying, ‘It will kill you — Warning.'” At an earlier rally, on the campus of Tennessee Tech University in Cookeville, Tenn., he added that the sign would be written “in English and in Spanish.”

“This nation has always been a nation with wide open doors,” Mr. Cain said at the second rally. “We want to make it easy for people to come through the front door. And we’re going to shut off the back door so you don’t have to sneak into America.”

Saying that some critics have told him that his remarks about building a fence are insensitive, Mr. Cain said that the fault lies with the actions of some illegal immigrants. “It’s insensitive for them to be killing our citizens, killing our border agents,” he said. “That’s what’s insensitive. And that mess has to stop.”

In addition using a fence and unspecified “technology” to cut down on illegal immigration, Mr. Cain added: “If we have to put troops with real guns and real bullets for part of it, we can do that too.”

Brent Wilkes, Vice Chair of the National Hispanic Leadership Agenda, said Mr. Cain’s remarks were reflective of increasingly harsh prescriptions for dealing with illegal immigration being offered by Republican presidential candidates.

“These folks who come across the border are at most committing a misdemeanor,” Mr. Wilkes said. “To suggest that they would be electrocuted or shot would be to treat them harsher than we treat murderers or rapists. It’s a real distortion of the rule of law.”

Mr. Wilkes said Mr. Cain is mistaken when he implies that it would be easy for would-be Mexican immigrants to enter the country legally. In fact, he said, there are few if any visas available for Mexican nationals who do not have a firm job offer in this country or who do not already have relatives living here legally.

After long being considered an also-ran in the Republican field, Mr. Cain has surged into the spotlight following his victory in the Florida straw poll and because of interest in his unusual 9-9-9 tax plan, which would set personal and business income tax rates at 9 percent each and institute a 9 percent national sales tax, eliminating all other federal taxes.

The Tennessee tour, which began Friday near Memphis, Mr. Cain’s birthplace, has drawn crowds of several hundred supporters and curious onlookers at each of eight stops.