Tánaiste Micheál Martin has said he wants to see Irish citizen Bernard Phelan released from jail as quickly as possible and that the Irish government has been "very clear" with Iranian authorities on this.
Mr Phelan, who also holds French citizenship, is one of two dozen foreigners who are being held in Iran, according to activists, who describe the detainees as "hostages" seized to extract concessions from the West.
The Paris-based travel consultant was arrested in October while travelling and is being held in Mashhad in northeastern Iran.
Iran accuses him of anti-government propaganda, a charge he has denied.
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Speaking on RTÉ's This Week, Mr Martin said he spoke with the Iranian ambassador last week and he has sought further engagement.
"We are hopeful of that early this week. We have made it very very clear to the Iranian authorities that Bernard Phelan should be released," he said.
Mr Phelan, who suffers from a heart condition and a chronic bone issue, suspended a hunger strike earlier this week.
The Iranian authorities have so far refused to release Mr Phelan on medical grounds despite repeated requests from the French and Irish authorities, a French diplomatic source said.
"We have stressed on humanitarian grounds we want him released. We are very concerned, we share the concerns of his family and we have made very strong representations to the Iranian authorities for his release on humanitarian grounds," Mr Martin added.
He said it is challenging in terms of the relationship between Iran and the EU.
"Diplomatic channels have always been maintained, engagement continues," he added.
He said there are a number of cases involving European citizens in Iranian jails which "is not acceptable".