The Associated Press left a message seeking comment from the Department of Homeland Security.
The lawsuit is the latest in a series of court filings challenging the Trump administration's decision to end the program for a cluster of countries whose citizens have lived and worked legally in the United States for years.
Last year, a federal judge in San Francisco temporarily blocked the U.S. government from halting the program for immigrants from El Salvador, Haiti, Nicaragua and Sudan. The suit filed on behalf of citizens of those countries, in addition to this one, cited Trump's vulgar language during a meeting last year to describe African countries.
The U.S. government grants temporary protected status, also known as TPS, to citizens of countries ravaged by natural disasters or war so they can stay and work legally in the United States until the situation improves back home.
The status is short-term but renewable, and some immigrants have lived in the country for decades, raising American-born children, buying homes and building careers.
Critics have said the program was meant to be temporary and shouldn't be extended for so long.
The Trump administration announced last year that the program would be ending for Honduras and Nepal. Honduras was designated for the program after a devastating 1998 hurricane, and about 86,000 immigrants from the country have the status, according to the lawsuit.
About 15,000 immigrants from Nepal — which was designated following an earthquake in 2015 — are covered, the suit said.
Together, these immigrants have more than 50,000 American-born children who would be affected by an end to the program, which lets those who are already in the United States stay in the country and obtain work permits, the suit said.
One of them is the 9-year-old daughter of Honduran citizen Donaldo Posadas Caceres, who came to the United States shortly before the hurricane in 1998. After Honduras was designated for the program, he obtained the status, and now works as a bridge painter and owns his home in Baltimore.
He said he doesn't want his children to return to a country they don't know and where life is so dangerous. His elder daughter, he said, is in college studying to be a lawyer, while the 9-year-old has plans of her own.