Boris Johnson made a “frank and constructive” start to his sensitive first trip to Tehran, where he will meet President Hassan Rouhani as he lobbies for the release of a jailed British-Iranian.

The foreign secretary’s visit comes as concerns grow about US president Donald Trump’s hostility to the landmark nuclear deal with Tehran, and deepening regional tensions, including over the Syrian war and Iran’s role in the conflict and humanitarian crisis in Yemen.

But Johnson is under closest scrutiny over efforts to secure the freedom of Nazanin Zaghari-Ratcliffe, arrested during a family visit with her infant daughter in 2016 and held in Tehran’s notorious Evin jail. Her fate has become entwined with Johnson’s own political career, after erroneous comments he made about her case were cited by Iranian officials pressing new charges that could double her prison sentence.

Zaghari-Ratcliffe is due back in court on Sunday, the same day Johnson will meet Rouhani. He is likely to make a personal plea to the Iranian president for her freedom, following up on a recent vow to leave “no stone unturned” in his efforts to secure her release.

Richard Ratcliffe, Zaghari-Ratcliffe’s husband, has not seen his wife since 2016 because he cannot get an Iranian visa. He said he was glad to hear initial talks described as “constructive”, and hoped his family might be reunited for Christmas.

“I am obviously watching closely with hope, fingers crossed and excitement – I couldn’t sleep at all last night,” Ratcliffe told the Press Association. Johnson himself has tried to downplay expectations of what the trip might achieve.

Johnson’s visit is only the third by a British foreign minister to Iran in the past 14 years, and the first since diplomatic ties were re-established in 2015.

It began with two hours of talks with the Iranian foreign minister, Mohammad Javad Zarif, which the Foreign Office said marked a “useful” start to the trip. The two men “spoke frankly about the obstacles in [their countries’] relationship, including the foreign secretary’s concerns about the consular cases of British-Iranian dual nationals,” a spokesman said.

The statement did not mention Zaghari-Ratcliffe by name, but she is the most prominent of several British-Iranians jailed in Iran. Johnson also met Ali Larijani, speaker of the parliament, and Ali Shamkhani, secretary of a powerful council that makes decisions on key national security issues and could potentially intervene in the case.

Zaghari-Ratcliffe was initially accused of attempting to orchestrate a “soft overthrow” of the Islamic republic and sentenced to five years in jail. She has always maintained her innocence and her employer, Thomson Reuters Foundation, has said she was not there to work and was on holiday. Then in November Johnson told the foreign affairs select committee that she had been in Iran to train journalists. Those comments were cited in a further Iranian court hearing as proof that she was engaged in “propaganda against the regime”.

After widespread outrage, he corrected his statement and apologised to the family, but insists that his remarks are not the reason Zaghari-Ratcliffe now faces a decade in jail. Hopes for a possible early release on humanitarian grounds grew last week when it was revealed that the Iranian government had ordered a health check. Her supporters say she has suffered panic attacks, insomnia, bouts of depression and suicidal thoughts, particularly after reports on her case on Iranian TV. She is taking antidepressants and other medication.

Johnson is expected to try to visit Zaghari-Ratcliffe in jail, and meet the head of the judiciary who is handling her case.

Conversations about her sentence are expected to be part of a wider discussion, including resolving banking restrictions that Iran says have made it hard for the country’s economy to benefit from the lifting of EU sanctions.

Johnson may be planning to use a disputed £300m payment that Britain owes Tehran to boost his negotiating position. The money was paid up front for a large order of tanks in 1976, but the fall of the Shah and subsequent embargo on arms sales to Tehran meant that only a few tanks were ever delivered. There is a strong case for a settlement now, as both sides have already given ground over the amount involved, and sanctions were lifted as part of the 2015 nuclear deal.

Downing Street insists there is no link between the money and Johnson’s efforts to secure Zaghari-Ratcliffe’s release. However, the US has admitted using a similar contested payout as leverage to secure the release last year of five American citizens held in Iran, in a prisoner exchange.