Gov. Ron DeSantis of Florida on Monday proposed a host of hard-right immigration policies, floating the idea of using deadly force against suspected drug traffickers and others breaking through border barriers while “demonstrating hostile intent.”

“Of course you use deadly force,” Mr. DeSantis said after a campaign event on a sweltering morning in Eagle Pass, a small Texas border city. “If you drop a couple of these cartel operatives trying to do that, you’re not going to have to worry about that anymore,” he added. He said they would end up “stone-cold dead.”

He did not clarify how Border Patrol officers or other law enforcement authorities might determine which people crossing the border were smuggling drugs. He said only that “if someone is breaking through the border wall” while “demonstrating hostile intent or hostile action, you have to be able to meet that with the appropriate use of force.”

Mr. DeSantis’s proposal served as an escalation of Republican messaging on the border and was part of a host of plans he unveiled in an effort to match the hard-line immigration stance of former President Donald J. Trump, who privately suggested shooting migrants in the legs during his administration.

Mr. DeSantis said that if elected, he would seek to tear down some of the pillars of American immigration law, such as the automatic granting of citizenship to those born in the United States.

And he said his administration would “fully deputize” state and local law enforcement officers in states like Texas to arrest and deport migrants back to Mexico — a power now reserved for the federal government — and to detain migrant children indefinitely, despite a court order imposing strict limits on the practice. He also promised to end “phony asylum claims.”

Those policies are sure to appeal to conservative voters in the Republican presidential primary contest, but they would be likely to run into legal roadblocks and could test the limits of presidential authority. The Constitution has been held to guarantee birthright citizenship, and the Supreme Court ruled in 2012 that states cannot enact their own immigration policy.

And while Mr. DeSantis argued that the country needed harsh new immigration rules because the current ones were encouraging dangerous border crossings and the mistreatment of migrant children, some of his proposals could also endanger migrants, including the use of “deadly force” against people cutting through the border wall.

“You do it one time and they will never do it again,” he said.

His campaign said in a news release that he would follow “appropriate rules of engagement” and that the rules would apply to “those trying to smuggle drugs into the United States.” (The overwhelming majority of drugs are smuggled in commercial vehicles coming across official ports of entry, not carried by migrants, according to U.S. border authorities.)

Another plan Mr. DeSantis put forward, which would require certain asylum seekers to wait in Mexico, was previously employed by Mr. Trump, drawing criticism for forcing migrants to live in squalid tent camps where some were reportedly subjected to sexual assault, kidnapping and torture.

Mr. DeSantis has made immigration a centerpiece of his campaign, but he has presented few specifics until now. Other policy proposals he released on Monday included:

• Deploying the military to “assist” Border Patrol agents until a wall is finished.

• Cracking down on Mexican drug cartel activity, including by blocking precursor chemicals used to manufacture drugs “from entering Mexican ports,” if the Mexican government does not act to stop the cartels.

• Detaining all migrants who cross the border without authorization until their immigration court hearing date. (Such a policy would most likely require the creation of a vast new prison system.)

“These are ideas that have rightly been categorized for a really long time as radical and extremist,” said Aron Thorn, a senior lawyer in the Beyond Borders Program of the Texas Civil Rights Project.

The policy rollout on Monday suggested that Mr. DeSantis, who is trailing Mr. Trump by roughly 30 percentage points in national polls, was trying to outflank the former president on immigration. Mr. DeSantis — whose “stop the invasion” language is a hallmark of America’s far right — has argued that he is the candidate most likely to enact conservative immigration policies. He has accused Mr. Trump of “running to the left,” saying that “this is a different guy today than when he was running in 2015 and 2016.”

But even among voters who came to see Mr. DeSantis on Monday at a cinder-block-and-steel Veterans of Foreign Wars post in Eagle Pass, some said that they remained more inclined to vote for Mr. Trump.

“He’s Trump 2.0, but this isn’t his time,” said John Sassano, 60, a retired teacher in Eagle Pass who described himself as a former Democrat. “I’d love to see him as V.P.”

Sandy Bradley, 66, a retired government worker, traveled with two friends from Del Rio, a nearby border town, to hear Mr. DeSantis, buying festive cowboy hats at a Walmart on the way. “I think he will catch up,” she said, adding that Mr. DeSantis seemed to share her Christian values.

She added that she wanted a candidate who would address illegal immigration and “stop all the influx.”

Mr. DeSantis went directly from the event to a news conference at a ranch along the Rio Grande outside town where the state of Texas had recently constructed fencing with concertina wire in an area where migrants often cross.

“This is an ongoing problem,” said Ruben Garibay, who owns the ranch. Mr. Garibay, wearing a black cowboy hat and speaking in the shade of a tree as the temperature neared 100 degrees Fahrenheit, said he had agreed to host Mr. DeSantis but had yet to make up his mind about which candidate to support. “It’s a little early in the game,” he said.

Mr. Trump first deployed a so-called Remain in Mexico policy, which the Biden administration later reversed. He also proposed ending birthright citizenship during his first campaign, although he failed to do so while in office, and has recently renewed those calls as a candidate. And, of course, he ran in 2016 on building a wall at the southern border, an issue that helped propel him to the White House.

On his social media site on Monday, Mr. Trump said that Mr. DeSantis’s “sole purpose in making the trip was to reiterate the fact that he would do all of the things done by me in creating the strongest Border, by far, in U.S. history.”

As governor, Mr. DeSantis last month sent hundreds of Florida law enforcement officers and Florida National Guard members to Texas, saying President Biden had failed to secure the border, a repeat of a similar effort in 2021 ahead of Mr. DeSantis’s re-election campaign.

This year, Mr. DeSantis also signed a bill cracking down on undocumented immigrants that was seen as one of the harshest such measures in the country. And he announced a national coalition of more than 90 local sheriffs who said they would band together to fight gang activity and illegal drugs that they argue are the result of the Biden administration’s border policies. (Only a few of the sheriffs are from border states.)

Some immigration analysts questioned the viability of Mr. DeSantis’s proposals, suggesting they were driven by the political imperatives of a presidential campaign.

“The bulk of the proposal is the usual laundry list of Republican talking points that have not been successful, either in Congress or in the court of public opinion,” said Louis DeSipio, a political scientist at the University of California, Irvine, citing the idea to end birthright citizenship, among other proposals. “The purpose is probably not a serious policy debate but instead to focus on an issue that is a weakness for Biden and a sensitive one for Trump.”

And Jennie Murray, the president of the National Immigration Forum, a nonprofit group that advocates immigration policies that address economic and national security needs, pointed to the difficulties in actually carrying out Mr. DeSantis’s plans.

“Deporting huge numbers of immigrants would be costly and extremely detrimental, especially during these times of historic labor shortages,” she said.

Miriam Jordan contributed reporting from Los Angeles.