Efforts to secure the release of the jailed British academic Matthew Hedges are continuing as the foreign secretary, Jeremy Hunt, called the United Arab Emirates’ foreign minister to discuss progress on his family’s appeal for clemency.

A Foreign Office spokeswoman said of Sunday’s call: “They had constructive talks and agreed to keep in close contact over the coming days.”

Earlier on Sunday, Hunt had said he was more optimistic than last week, but the Foreign Office was not expecting an immediate breakthrough. The UAE foreign minister, Sheikh Abdullah bin Zayed Al Nahyan, will be critical to any potential decision to release Hedges, who was sentenced last week to life imprisonment for espionage. His family have described the charge as absurd, and say he was doing legitimate academic research in the UAE as part of a PhD at Durham University.

There has been speculation the UAE could release Hedges on its national day, 2 December.

The president, Sheikh Khalifa, ordered the release of 785 prisoners on Sunday ahead of the national day and also paid off their fines. There was no word whether Hedges was included in this group.

The Hedges family had pleaded for clemency last week, and hoped Hedges would be included in the releases. He was detained at Dubai airport on 5 May and has been kept in solitary confinement for the bulk of the past six months. His wife, Daniela Tejada, has complained the Foreign Office did little to secure his release until she mounted a public campaign to highlight the treatment of her husband by one of the UK’s closest Gulf allies. She has launched an online petition to secure his release, and a growing number of universities are reviewing their links with the UAE.

Hedges lodged an appeal last Wednesday and a hearing must be held within 30 days.

The purpose of the pardons, according to the UAE state news agency, is to offer detainees the opportunity to “create a new life for themselves and alleviate the suffering of their families”. Every year, the country’s rulers pardon prisoners and order debt settlements of those jailed for financial crimes or with outstanding fines.

Prisoners are selected on the basis of their good conduct. Last year, the UAE pardoned about 2,000 people.

Without going into details, Hunt told BBC One’s The Andrew Marr Show on Sunday: “I am more optimistic as we sit here now that we can find a way through this. The UAE is a very longstanding friend of the UK and I’ve had very good conversations with their foreign minister; I am going to speak to him again this afternoon.”

The sheikh spoke with Hunt on Friday in what was described as a positive call, but influential UAE academics continued to defend the sentence on Sunday, suggesting there is resistance to his release.

Abdulkhaleq Abdulla, a professor of political science, said on Twitter: “The case against him is crystal clear. He admitted the charges. The evidence is irrefutable and the UK government does not deny it. Now he wants clemency.”

At the weekend, the UAE foreign minister made no mention of Hedges during a lengthy speech highlighting the country’s ties with the EU at the opening of an exhibition in Abu Dhabi celebrating the UAE-EU relationship.

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The exhibition coincided with the Formula One Grand Prix in Abu Dhabi, which was attended by the Saudi crown prince, Mohammed bin Salman. The crown prince met with the nephew of Jamal Khashoggi, the Washington Post journalist killed by a Saudi Arabian hit squad in the Saudi consulate in Istanbul in October.

Khashoggi’s nephew posted an Instagram picture at the weekend of him posing for a picture with the crown prince.

Marr also asked Hunt if there were any grounds for optimism in the case of Nazanin Zaghari-Ratcliffe, a project manager with the Thomson Reuters Foundation who was arrested in April 2016 in Tehran as she headed back to Britain with her daughter, now aged four, after a family visit.

She was sentenced to five years in jail after being convicted of plotting to overthrow Iran’s clerical establishment, a charge denied by her family and the foundation. “I think that’s more challenging,” Hunt said. “I was in Tehran on Monday, and I asked to meet Nazanin. I wasn’t allowed to but I did meet her daughter.”

Hunt said he had urged Iran to provide medical assistance to Zaghari-Ratcliffe and to another, unnamed, citizen in a similar situation. He said it was “totally and utterly unacceptable” for Iran to “start locking up innocent people as a tool of diplomatic leverage”.

He asked the Iranian foreign minister, Mohammad Javad Zarif, to give Zaghari-Ratcliffe a copy of Nelson Mandela’s Long Walk to Freedom, which he had taken to Tehran for her.