Former President Donald Trump said Vice President Kamala Harris should be barred from the White House because the Biden administration’s approach to immigration turned the U.S. into a global “garbage can” for murders and violent gangs.

Mr. Trump told voters in Arizona that if elected, he would expand upon the moves he made as president to “stop all illegal immigration once and for all.”

He is promising the “largest domestic deportation operation in American history,” mandatory 10-year prison sentences for repeat border jumpers, and the mandate of the death penalty for illegal immigrants convicted of murdering U.S. citizens.

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“Kamala’s migrant invasion — given to us through gross incompetence — disqualifies her from even thinking of being president,” Mr. Trump said at the campaign rally. “No person who is responsible for so much bloodshed and death on our soil can ever be allowed to become the president of the United States.

“When we win on Nov. 5, the migrant invasion ends, and the restoration of our country begins,” Mr. Trump said. “The United States is now an occupied country, but it will soon be occupied no more.”

He said Election Day will be “liberation day.”

With the final week of campaigning around the corner, battleground state polls and political pundits suggest the contest is tight.

President Biden carried Arizona in 2020 by fewer than 11,000 votes. The state became ground zero for Mr. Trump’s false stolen election claims.

Mr. Trump has switched up his message this time. Four years after disparaging the practice as rife with fraud and corruption, he urges his supporters to take advantage of early voting.

“Get everyone you know and vote,” he said Thursday.

Mr. Trump has anchored his campaign on immigration and border security, issues that are top of mind for many voters, including Hispanic voters — particularly in border states such as Arizona.

He has blamed the Biden-Harris administration for making a mess of the strong border it inherited. He highlights how more than 13,000 immigrants convicted of homicide are roaming freely across the nation. 

At another Arizona rally last week, Mr. Trump received the endorsement of the National Border Patrol Council.

Mr. Trump has a slight edge in Arizona and is outpacing Ms. Harris among Hispanic voters in the border state. Ms. Harris leads among independents.

Arizona voters also will have the final say in the race between Rep. Ruben Gallego, a Democrat, and Kari Lake, a Republican. They are vying for the seat held by Sen. Kyrsten Sinema. The Democrat-turned-independent decided against reelection after falling out of favor with the party’s base.

Voters also will consider a referendum to the state constitution that would enshrine a woman’s right to have an abortion.

Earlier Thursday, Mr. Trump said he would fire special counsel Jack Smith in “two seconds” if he wins The White House.

Mr. Smith has been a central figure in the federal cases involving Mr. Trump.

“I would fire him within two seconds. He’ll be one of the first things addressed,” he said. 

When asked if he was ready to possibly get impeached for the third time if he got elected and fired Mr. Smith, Mr. Trump dismissed that idea.

“No, I don’t think they’ll impeach me if I fire Jack Smith. Jack Smith is a scoundrel. He’s a very dishonest man, in my opinion, very dishonest man,” he said.

• Mallory Wilson contributed to this report.