President Donald Trump is facing calls from business leaders to “turn the page” on his immigration crackdown after a raid at a Hyundai plant in the US state of Georgia.

It was the largest such raid in US immigration history, sweeping up 475 workers, including about 300 people from South Korea.

The decision to target the project, backed by a company the president has celebrated for putting money and factories in the US, sparked shock and outrage in South Korea, where politicians and business leaders have warned it will chill willingness to invest in the US.

In the US, business groups said the raid was likely to hit local business activity as well, as it scares off key parts of the workforce.

“Those actions are having ripple and ancillary effects on others, real and unintended, unfortunately whether they’re in legal status or not,” said Jeff Wasden, president of State Business Executives, which represents state lobby groups from businesses across the economy.

He said he had emailed the White House on Monday, hoping the moment provided an opening to shift from enforcement to fixes to the US immigration system.

While praising Trump for stopping the flow of migrants across the border, he said the raids were generating “fear” and “dampening” US economic activity.

“We’ve got to turn the page,” he said. “It’s time to focus on the workforce and how we fix some of these programmes and problems.”

Since the raid, construction at the site, a partnership between Hyundai and LG Energy Solutions that will make batteries for its electric cars, has halted.

LG and other top South Korean firms have also put new limits on business travel to the US, according to South Korean media.

South Korean officials have indicated that many of those detained who were from South Korea had entered the US on temporary visas that allow workers to visit for business meetings or conferences, but not paid employment in the US.

Such visas have been a common workaround used by businesses in the country, which have long been frustrated that they do not benefit from a more expansive visa programme, like one currently enjoyed by countries such as Australia.

Many Trump supporters oppose loosening visa rules, arguing that such programmes have been used by big business to import cheaper foreign workers and freeze out American citizens.

But as the US pushes to reshore industries such as semiconductors, trade groups say there are not enough workers with the necessary skills in the US.

In a statement to the BBC, Jae Kim, president of the Southeast US Korean Chamber of Commerce, a group aimed at boosting ties between South Korea and the south-eastern US, said it was “not an easy process” for foreign firms to secure visas, especially for temporary workers.

He warned that the hold-ups made it “hard to make such next generation manufacturing projects prosper in the US” and urged a “stronger balance” of US priorities.

In remarks to reporters over the weekend, Trump has acknowledged the complaints about the visa process, telling reporters: “We’re going to look at that whole situation.”

In a follow-up post on social media, Trump said foreign investments were “welcome”, but called on foreign companies to “please respect our Nation’s Immigration Laws”.

“We encourage you to LEGALLY bring your very smart people, with great technical talent, to build World Class products, and we will make it quickly and legally possible for you to do so,” he wrote on Sunday, adding: “What we ask in return is that you hire and train American Workers.”

But it’s not clear to what extent the administration plans to alter its approach.

In an appearance on CNN on Sunday, border czar Tom Homan said more worksite raids were coming.

Trump has previously confronted tensions between his promises to ease the way for business and his aggressive immigration policies.

Before he even took office, his supporters broke out in a bitter online brawl about whether the administration should make it easier for companies to secure visas for high-skilled tech workers.

The fight pitted Elon Musk and other tech gurus who had supported his campaign against former Trump campaign manager Steve Bannon.

Cracks in the coalition emerged again this June, as the White House stepped up its worksite raids, drawing outcry from farmers and hotels. The administration suggested it would modify its approach, only to reaffirm crackdown a few days later.

Jennie Murray, chief executive of the National Immigration Forum, a group that advocates for immigrants and has been involved in discussions about reforms, said the recent messages from the White House had been “mixed”.

But she said some top Trump officials, including those from the labour and agriculture departments, had been receptive to business concerns about workplace raids, which previous presidents have largely avoided due to their controversy and economic costs.

She said she saw those arguments making inroads, especially as economic costs of raids like the one in Georgia become evident.

“The impact is starting to speak for itself,” she said. “As the economy continues to take hits and really starts to slow, which is likely going to happen in the next couple of months, I think there are a lot of folks who are willing to have conversations about what those solutions are.”

But Douglas Holtz-Eakin, president of the American Action Forum, a center-right policy institute, said he had seen little sign that the administration was preparing to change its approach.

He added of the president: “He’s highly tuned to pressure. If the pressure becomes large enough, he’ll alter the policy but we haven’t seen that yet.”