Donald Trump – who has built his presidential campaign on the idea that immigrants are “destroying” the US and promoting mass deportation – faced blunt, tough questions from undecided Hispanic voters on Tuesday.

At a town hall hosted by Univision, the largest US Spanish-language network, several dozen Latino voters from across the country questioned the former president about immigration, as well as the economy, abortion and other key issues.

The Republican presidential candidate – who has been increasingly trying to court Latino voters – struggled to field specific questions about policy, even as he doubled down on misinformation about immigration.

Polls have indicated that Trump is making inroads with Hispanic voters, who – like multiple other demographic groups – say they favour the former president on economic issues. Latino voters are an increasingly important voting bloc in several swing states. At the town hall, in front of 100 voters, Trump did not mention his plans to order the largest mass deportation in US history.

He also dodged or dismissed tough questions about his rhetoric and policies concerning immigrants. When a voter, who mentioned he was a registered Republican, asked why Trump keeps repeating the debunked myth that Haitian immigrants are eating pets in Springfield, Ohio, Trump doubled down.

“I was just saying what was reported,” Trump said – adding that migrants were “eating other things too, that they’re not supposed to”.

Guadalupe Ramirez, whose parents immigrated from Mexico, asked Trump for more details about his proposals and asked why he had urged legislators to vote against a bipartisan immigration reform bill. Trump provided no details, but instead criticised Democratic leaders, including the governor of Illinois, alleging that migrants were driving up crime, and boasted that he had the “strongest border”.

When Jorge Velázquez, a California farmworker, asked bluntly who would do the backbreaking labor of harvesting America’s fruit if Trump were to deport the many undocumented workers who currently do the job, the former president dodged.

He accused newer immigrants of stealing jobs from Hispanic people in the US, and characterised migrants – as he often does – as “hundreds of thousands of people that are murderers, drug dealers and terrorists”.

“We have to have people that are great people come into our country,” he said. “I want them in even more than you do.” But he never directly addressed deportations.

During her town hall with Univision, Kamala Harris highlighted her policies to address inflation and protect abortion rights. She also warned that her opponent was sowing misinformation and division.

“I know that the vast majority of us have so much more in common than what separates us, and part of what pains me is the approach that frankly Donald Trump and some others have taken, which is to suggest that it’s us versus them … and having Americans point fingers at each other, using language that’s belittling people,” she said.

“I don’t think that’s healthy for our nation, and I don’t admire that.”