Iranian authorities unexpectedly granted Swiss diplomats permission this past week to visit an American Navy veteran held in a prison in the country’s northeast, where they learned his cancer had recurred, his mother said Saturday.

The prisoner, Michael R. White, 47, one of at least four Americans known to be jailed in Iran, has had throat cancer. He was visiting an Iranian female friend in the northeastern city of Mashhad when he was seized more than a year ago, in July 2018.

Mr. White, of Imperial Beach, Calif., was tried and convicted on charges that included insulting Iran’s supreme leader and posting private photographs on social media. He was sentenced in March to 10 years in prison, and Iranian prosecutors suggested he might be charged with espionage.

“I’m at my wits’ end,” said his mother, Joanne White, who has not been able to talk with Mr. White since his imprisonment and has been communicating through Swiss diplomatic intermediaries. “I am afraid he will die there if nothing is done to bring him back.”