Ahmed Abdulwahab’s family has survived airstrikes and firefights. They endured daylong drives across crumbled roads and on mountain ledges so steep it felt as if gravity would surely bring them tumbling down.

Mr. Abdulwahab has crossed into Yemen territory controlled by various factions: Al Qaeda, Houthi rebels and the government, all to get his wife, mother and young daughter out of the country and into the United States. An American citizen, Mr. Abdulwahab described the weekslong journey as the most terrifying travel of his life.

But now he’s up against one final obstacle: the United States State Department.

Mr. Abdulwahab, 32, is one of hundreds of Yemeni-Americans in New York who were separated from non-U. S. citizen spouses or children following the Trump administration’s so-called travel ban, which severely restricts entry into the United States by people from seven countries, five of them Muslim-majority.

Some, like Mr. Abdulwahab’s wife, Aisha Mahyoub, 30, were approved for a visa only to have it revoked once the ban went into effect. Such an action violated the terms of the ban, according to a lawsuit filed on Monday by the Center for Constitutional Rights, a legal advocacy organization based in New York. Three other Yemeni-Americans are involved in the case, which follows a similar class-action suit filed in September on behalf of more than 100 others.