Foreign Secretary Boris Johnson held two hours of "frank" talks with his Iranian counterpart Mohammad Javad Zarif, which also touched on the landmark 2015 nuclear deal between Tehran and world powers, the future of which has been thrown into doubt by US President Donald Trump.
Mr Johnson's meeting with Mr Rouhani was seen as a positive move, considering the usually hard relations with the country.
"The two sides discussed various matters including economic, banking and trade relations", the Iranian Foreign Ministry said in a statement.
When the couple last spoke by telephone on Tuesday, Mrs Zaghari-Ratcliffe was "genuinely anxious about the court case and getting quite agitated", her husband said.
Johnson is in Tehran as part of a three-nation Gulf tour, which the Foreign Office said was focused on the Iran nuclear deal and "how to bring an end to the conflict in Yemen".
However Tehran does not recognise Mrs Zaghari-Ratcliffe's dual UK-Iranian nationality, and refuses access to her for representatives of the British authorities, making a prison visit for the Foreign Secretary unlikely during the trip.
Johnson has vowed to leave "no stone unturned" in Britain's efforts to free Zaghari-Ratcliffe, a project manager with the Thomson Reuters Foundation, who was sentenced to five years in prison after being convicted by an Iranian court of plotting to overthrow the clerical establishment.
"While our relationship with Iran has improved significantly since 2011, it is not straightforward and on many issues we will not agree", Johnson said ahead of the trip. Johnson told Zarif he believed the deal should be fully implemented.
Israeli force attack a student demonstration in Bethlehem
The Israeli military claimed to hit a weapons manufacturing site and an ammunition store early today. Shortly afterward, air raid sirens sounded again as another salvo of rockets was launched.
The Thomson Reuters Foundation, a charity organization that is independent of Thomson Reuters and operates independently of Reuters News, said Zaghari-Ratcliffe had been on holiday and had not been teaching journalism in Iran.
Mrs Zaghari-Ratcliffe's sister-in-law, Cwmbran GP Rebecca Ratcliffe recently acknowledged that the political pressure by the government had increased.
Hopes for Mrs Zaghari-Ratcliffe's early release rose earlier this month when it emerged an Iranian government medic was to make checks on her mental health after claims she has been suffering panic attacks, depression and suicidal thoughts. Her family has denied the allegations.
Meanwhile, the BBC urged Johnson to raise their complaints about the "harassment and prosecution" of their Persian-language staff living overseas.
Zaghari-Ratcliffe has been told she will appear in court on December 10, her husband Richard has said.
BBC Persian staff have had their Iranian bank accounts frozen, and complain of threatening phone calls and interrogations of family members in Iran.
Global sanctions against Iran have only recently been lifted as part of the multilateral nuclear deal to curb Tehran's disputed uranium enrichment programme.
The visit will be sandwiched between meetings in Oman and the United Arab Emirates as Johnson - a key proponent of Britain's exit from the European Union - takes advantage of a gap in a domestic parliamentary calendar dominated by Brexit.