“We must first take care of the American worker,” President Trump said, insisting that newly jobless citizens should not have to compete with foreigners when the economy reopens.

Rights groups say the immigration process has become increasingly complex and frustrating in recent years, with Mr. Trump fanning the flames of anti-immigrant sentiment by pushing for an extensive wall along the Mexican border and labeling a group of African nations “shithole countries.”

For Indian citizens, building a more permanent base in the country was never easy.

Most of the 800,000 immigrants currently waiting for a green card are Indian citizens. Because of quotas that limit the number of workers from each country, Indians can expect to wait up to 50 years for a green card since their representation among immigrants is so high in the United States.

Last summer, the Fairness for High-Skilled Immigrants Act, which sought to address the backlog by eliminating country quotas, sailed through the House. But it stalled in the Senate, where critics like Senator Dick Durbin, Democrat of Illinois, argued that the bill would not solve the problem because it does not increase the overall number of green cards.

Many Indian citizens said the back-and-forth was exhausting.

“I likely won’t receive a green card in this lifetime unless the laws change,” said Somak Goswami, an electrical engineer who applied for a green card in 2011. “I have colleagues who came to the U.S. in 2017 and have a green card already. My only fault was I was born in India.”

Analysts said immigration restrictions could strain the delicate but increasingly amicable relationship between India and the United States, the world’s most populous democracies.