By Liz Robbins, The New York Times

A Flatiron district artificial intelligence start-up was recently looking to expand, adding new engineers who happened to know a niche computer language.

The people it hired hail from Morocco, Belarus, France, Georgia and Canada. But they are not working in New York. They are in Montreal, where immigration policies make it possible to get work permits within two weeks, and the Canadian tech industry is aggressively trying to woo foreign companies.

“It’s becoming less and less sexy to be going to the United States,” said Tim Delisle, 26, a founder of the start-up Datalogue, which uses artificial intelligence to prepare and synthesize data for other businesses. He added that skilled foreign workers crave the greater stability that he said immigrants have in Canada compared with the United States.

While much attention has been paid to President Trump’s policies cracking down on illegal immigration, the administration has also moved to restrict legal immigration, especially in the tech industry, which draws many workers from abroad. In April, Mr. Trump introduced an executive order, Buy American and Hire American, which included requests to reform a visa program known as H-1B as a way to benefit American workers.

The program awards 85,000 temporary visas annually to highly skilled foreign workers in what are deemed “specialty” occupations through a lottery. Between application and legal fees, the process of applying for one H-1B visa can cost a company up to $6,000, lawyers say, and can take months; it is also as uncertain as roulette, with hundreds of thousands of applicants for the spots.

Last week, the Department of Homeland Security published a set of proposed rule changes that would make the visas even harder to qualify for, to ensure that only “the best and brightest” foreign workers were selected. It also hoped to eliminate a work permit for spouses of some of these visa holders.

In contrast, Canada’s immigration agency in June started the Global Skills Strategy for high-skilled workers from abroad to get a work permit in two weeks.

“That is, excuse my English, goddamn fast,” said Hubert Bolduc, the chief executive of Montreal International, a public-private partnership that recruits foreign companies to move to Canada and offers support once they arrive in Montreal. “We’ve been loving government on this because we know it’s a talent game.”

In 2017, the organization conducted eight international recruiting missions, in London, Paris, San Francisco and Los Angeles. Its directors have made several informal visits to New York, where it came this month to woo a video game company.

With the Trump administration’s immigration policies, “We’re almost saying, ‘Don’t come,’” said Sunil Hirani, the co-founder of trueEx, an electronic global interest rates exchange, also in the Flatiron neighborhood. He came to New York as a child 40 years ago from India. “How can you have a ‘Come to New York City’ program if the people of New York City are going to get kicked out? How do you sell that?”

Last year, trueEx’s chief executive and president, Karen O’Connor, was looking at options to expand the company’s computer engineer group. A consortium related to Montreal International invited her to Canada for a visit that made her feel like a foreign dignitary, she said. There was the elegant lunch, the precisely coordinated meetings with potential business partners and a visit to the Montreal Stock Exchange.

Ms. O’Connor said the 50-person company could save more than $1 million in wages if it hired engineers based in Montreal. In part, that was because the cost of living was far less compared with New York and because the company could qualify for certain tax benefits.

But after Mr. Trump was elected, trueEx hesitated, to gauge the climate; now, it is again considering expanding north of the border in 2018, Ms. O’Connor said, in part because it got a spot site visit from the Department of Homeland Security this summer to verify employment records for its H-1B visa holders. They were in order, but the company’s executives found the process nerve-racking.

“My advice to other companies would be: Hold on for dear life, but explore other options,” Mr. Hirani said.

But John Miano, a lawyer who represents American workers who say that they have lost jobs unfairly to low-skilled H-1B visa holders, thought it was “posturing” for companies to say they are moving north of the border to find the best talent. “The problem is, you got to go to Canada,” Mr. Miano said. “The reality is, the place to do business is still the United States.”

Datalogue’s expansion to Montreal, Mr. Delisle’s hometown, evolved swiftly. He and a partner founded Datalogue in 2016 at Cornell Tech in Manhattan and were lucky when a tech mogul, Charles E. Phillips Jr., the chief executive of Infor, gave him two desks on the fifth floor of Infor’s elegantly restored Flatiron headquarters.

By spring 2017, Datalogue had grown to five employees and had raised $1.5 million in seed funding. But to bring in more engineers would have cost thousands of dollars in visa fees, Mr. Delisle said, and even then, the process would not be guaranteed. Canada has a burgeoning artificial intelligence sector, and the company opened its Montreal office in April in the trendy Mile End neighborhood; it raised another $1.5 million in seed funding by November.

Still, Mr. Delisle said that his company has better access to customers in New York, and for that reason he has kept seven employees there for sales and marketing.

While tech is still thriving in New York, where it is the fastest-growing industry in the city, losing offices or whole companies to Canada could be a concern, said Kevin Ryan, an entrepreneur who had founded a half-dozen start-ups. The multiplier effect of the start-up world is a powerful one.

“When someone decides not to come here to join a start-up, and they go to Toronto, some of them may break off and start a new company across the street,” he said. “The wider impact will be felt, literally, for decades.”

Mr. Delisle agreed. “I’m not necessarily scared for New York; there’s phenomenal programs there,” he said. “I am more scared for the broader policies being applied right now.”

According to the Partnership for New York City, a business advocacy group, immigration has always been central to the economy of New York. Forty-eight percent of the city’s small-business owners are immigrants, and 45 percent of the work force in the city is foreign-born.

“The No. 1 priority of business today is where they can get the talent they need from the global talent pool,” said Kathryn S. Wylde, the chief executive of the group. “There’s not much a locality can do to incentivize, but we can try to keep the global pipeline open.”

Stimulating the city economy was the impetus for New York City’s Economic Development Corporation to create a program called International Innovators Initiative, or IN2NYC. The idea was to provide H-1B visas that were exempt from the government-imposed cap because entrepreneurs would work in partnership with city universities.

The program was announced in the spring of 2016 and received 144 applications in the first round. The second round, coming on the heels of the Trump administration’s travel ban, attracted half that number. The program received only 41 this fall.

Perhaps even more telling is the small number of foreign entrepreneurs who received visas: six. The IN2NYC program had envisioned at least 25 working at once, but the process, officials say, has been delayed by government challenges to the visas.

One company that was initially rejected has appealed — and set up shop in Canada while it is waiting for a decision.