To make their case to the Pentagon, recruiting officers compiled dossiers on the first class of immigrants, of whom 943 out of 1,000 were in the Army. On average, immigrants who enlisted in the Army language program scored 17 points higher (on a scale of 99) than other applicants on an entrance test, said Capt. Carol Stahl, who manages the program for the Army. One-third of the first class of recruits had master’s degrees or higher.

One-third of the class went into the Special Forces, a highly selective assignment that can often lead to combat missions, Captain Stahl said. Attrition was one-quarter the rate of other soldiers who entered at the same time.

A soldier from Nepal who entered with the first class, Sgt. Saral Shrestha, just won the Army’s Soldier of the Year award after a grueling four-day competition involving fighting skills at Fort Lee, Va.

“This was a boost of very high quality people,” said Margaret Stock, an immigration lawyer in Alaska who is a retired lieutenant colonel in the Army Reserve and helped devise the program. Even before they enlist, she said, the immigrants have been screened because they have to pass background and occupational checks for their temporary visas.

To qualify, immigrants must have been living in the United States legally for at least two years. They must be high school graduates and pass the entrance test.

The program — known as Military Accessions Vital to the National Interest, or Mavni — is not open to illegal immigrants, who are barred by law from enlisting. In general, immigrants who are not citizens must have a permanent resident visa, known as a green card, to enlist.

The first round filled up quickly, and the Army turned away thousands of people. Many of them signed the Facebook petition and were hoping the program would start again.