UK Foreign Secretary Boris Johnson has had a "worthwhile visit" to Iran and met President Hassan Rouhani on a second day of talks in the country.
A Foreign Office spokesman said both "spoke forthrightly" on several issues, including the case of jailed British-Iranian Nazanin Zaghari-Ratcliffe.
The mother-of-one has been held in Iran since April 2016 on charges of spying, which she denies.
She was not required to appear at an expected court case on Sunday.
It had been thought she would appear in court on fresh charges, but her husband Richard Ratcliffe has confirmed that the case was not held.
"Of course, one swallow doesn't make a Christmas - Nazanin is not yet on a plane. But it is good to have at least a swallow in the sky," he said.
The head of Iran's Revolution Court, Hojjat ol-Eslam Mousa Ghazanfarabadi, confirmed no court hearing was held for Mrs Zaghari-Ratcliffe on Sunday.
On Saturday Mr Johnson urged his Iranian counterpart to release Mrs Zaghari-Ratcliffe and other dual nationals on humanitarian grounds.
In two hours of talks, Mr Johnson and Mohammed Javad Zarif also discussed "the obligations of all parties to implement the nuclear deal", Iran's foreign ministry said.
US President Donald Trump has made his opposition to the deal, struck in 2015, very clear and has threatened to scrap it. But the UK continues to support it.
In October when Mr Trump threatened to tear the deal apart, the UK, France and Germany said it was "in our shared national security interest" that its arrangements continued.
A Foreign Office spokesman said: "We leave with a sense that both sides want to keep up the momentum to resolve the difficult issues in the bilateral relationship and preserve the nuclear deal."
On Saturday, Mr Ratcliffe, who has been campaigning for his wife's release, said he hoped Mr Johnson would be "persuasive and charming and build a good relationship".
It is thought that Mrs Zaghari-Ratcliffe faces a possible court appearance later on new charges.
BBC diplomatic correspondent James Robbins said the president's powers were limited because he is not Iran's supreme leader.
Meeting can be seen as a positive
Analysis by the BBC's diplomatic correspondent James Robbins
The mere fact of Boris Johnson spending nearly an hour with President Hassan Rouhani can be seen as a positive.
The Foreign Office says a "full range of issues" were discussed including "concerns about the consular cases of dual nationals".
Banking matters were also on the agenda, including:
- An outstanding debt of £400m owed by Britain to Iran. Britain says the money is ready to be paid when a method of doing so can be found which doesn't break international sanctions
- Iranian anger that no British bank will open an account for Iran's embassy in London
- Iran's judgement that British banks and businesses are dragging their feet getting involved in Iran after the relaxation of many restrictions with the signing of the nuclear deal
Neither side is linking any of this to the appeal for prison releases, but the Foreign Office said the delegation was leaving Iran with a sense that both sides "wanted to resolve the difficult issues in the relationship".
Mrs Zaghari-Ratcliffe was arrested on a visit to see her parents with her infant daughter Gabriella.
After the arrest, her daughter's passport was confiscated and for the last 20 months the three-year-old has been living with her maternal grandparents in Iran.
Iran does not recognise Mrs Zaghari-Ratcliffe's dual citizenship and will not allow UK representatives to see her in prison.
The case was further complicated when Mr Johnson told a parliamentary committee in November that Mrs Zaghari-Ratcliffe had been in Iran to train journalists.
The foreign secretary later apologised in the Commons, retracting "any suggestion she was there in a professional capacity".
Last month, the Free Nazanin Campaign said Mrs Zaghari-Ratcliffe had suffered panic attacks, insomnia, bouts of depression and suicidal thoughts and had been given a health assessment.
On Saturday, Mr Ratcliffe said he believed the foreign secretary's presence in Iran would "make a difference", but the situation remained very unclear.
"It's all up in the air," he said. "We're holding on to the good bits - it could go any which way.
"Fingers crossed it can be solved by Christmas, which means in the week or so afterwards there might be a happy outcome."
The Foreign Office would not confirm the names or number of other dual nationals being held, saying their families had asked for their cases to be kept out of the public domain.
Relations between the UK and Iran have long been difficult. Mr Johnson's visit is only the third by a British foreign minister to Iran in the last 14 years.