She was tried and sentenced to five years in prison on charges of sedition after she was accused of plotting a “soft toppling” of the government, according to the foundation. Her relatives denied the accusation.
Earlier this year, Mr. Johnson infuriated those working to free Ms. Zaghari-Ratcliffe by saying she had been “simply teaching people journalism” in Iran, something her employer, her relatives and her local parliamentary representative in Britain said was untrue.
Mr. Johnson later apologized, saying his statement had been a mistake.
On Sunday, Mr. Ratcliffe, who had lobbied to accompany Mr. Johnson on the trip to Iran, said he was pleased with what the foreign secretary had been able to accomplish.
“A month ago I was cursing the foreign secretary,” he said, “but he promised when we met that he would do his best for Nazanin, and to date he has been as good as his word.”
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Ms. Zaghari-Ratcliffe, who has been allowed to make phone calls from prison, was quoted by the British broadcaster Sky News as saying she “can see some light today.”
Mr. Johnson’s three-nation trip to the Middle East took him to Oman on Friday, and he was expected to visit the United Arab Emirates next.
He met with Iran’s president, Hassan Rouhani, on Sunday after meeting with the foreign minister on Saturday. No details of their talks were released. But the British Foreign Ministry issued a statement saying both men “spoke forthrightly about the obstacles in the relationship and agreed on the need to make progress in all areas.”
Among the “difficult issues” they discussed were ways to preserve the Iran nuclear deal that President Trump has derided as the “worst deal” and “an embarrassment.”
Britain is also considering settling a longstanding debt to Iran by repaying about 400 million pounds, or about $537 million, from a pre-1979 arms deal involving hundreds of Chieftain tanks that were never delivered.
Mr. Johnson left without a clear conclusion to the long-running dispute over the arms deal, which some analysts suggest could be used to help secure a release.
But both Britain and Iran say a repayment would not be tied to Ms. Zaghari-Ratcliffe’s case, though the United States made a similar payment to Iran in 2016, around the time that four American citizens, including The Washington Post reporter Jason Rezaian, were released.
Iran’s judiciary announced this year that more than 30 dual nationals were being held in the nation’s prisons, several on charges of spying.