Julie Goldberg, a lawyer in Djibouti, said hundreds of people had come to her doorstep since mid-December. She estimated that more than 300 Yemeni nationals had been rejected so far. “There’s no explanation for getting denied — everybody’s getting denied,” she said in a telephone interview from her home there, which serves as a legal clinic. “It’s complete hopelessness. I have women sobbing.”

But the State Department said there was an explanation: However final it may seem, an approval notice is not a guarantee, said an official with the department who spoke anonymously because its employees are not authorized to speak publicly. Such a notice should have been considered provisional, the official said, because at the time, the vetting of the would-be immigrants was not yet complete. The ban’s assurances, the official said, applied only to those holding actual visas.

But the notice — with the case number written in pen to identify the visa applicant — seemed like the last word to the immigrants and those working on their behalf. “We looked at it like that for all of our clients,” said Mosheer Fittahey, a consultant for Marhaba Service in Albany, which assists Yemeni nationals in legal, financial and travel transactions.

Mr. Fittahey said 111 Yemeni-Americans from across the country have contacted him on behalf of their relatives who received approval notices followed by rejections from the embassy in Djibouti. More calls come daily. About 60 percent of the cases there involve women and children, he said.