More than 7,000 people from Northern Ireland applied for Irish passports last month, the Irish Government has confirmed.
Total applications for June, including the week after the Brexit referendum result, soared by almost 10%.
And in addition to the 7,045 applications from here, there were also more than 5,700 from Britain - up by around 20%.
Now the Irish Senate is to consider the establishment of an Irish passport office in Northern Ireland to help cope with the demand.
Sinn Fein said yesterday it expected the totals to rise in the coming months.
Some local post offices ran out of application forms in the immediate aftermath of the UK voting to leave the European Union last month.
Former Belfast Lord Mayor Niall O Donnghaile, who is now a member of the Senate at Leinster House, said a passport office for local applications was a logical development.
His comment came after the Republic's Minister of State Joe McHugh revealed the figures.
Senator O Donnghaile said an Irish passport office was needed on this side of the border "in order to greater enfranchise people across Ireland and also to ease the burden on staff".
"The substantial existing demand for Irish passports in the North has only increased following the result of the Brexit vote. These figures are only set to rise further.
"That is why a passport facility in the North makes practical sense."
The senior Sinn Fein politician said he had been encouraged to hear the minister approach the matter from a "positive and resolute frame of mind". "I share that approach," he added.
"I will continue to engage him, his officials, community, business and civic leaders from right across the North on ensuring this facility can be realised in order to greater enfranchise people across Ireland and also to ease the burden on staff."
But the DUP's Christopher Stalford called the clamour for Irish passports a "knee-jerk" response to the Brexit vote and argued Dublin wouldn't make a move as regards an office based on applications made in just one month.
The South Belfast MLA accused Sinn Fein of playing politics over the issue.
"It is a matter for individuals whether they apply for an Irish passport or not, but many of us will continue to travel on our British passport," he said.
"The increase in applications for Irish passports is likely to have been one of the knee-jerk reactions following the referendum result.
"The Irish Government is unlikely to take any decision on the basis of an increase in one month. It is disappointing that Sinn Fein's contributions following the referendum have been stunts and posturing.
"What we should be focusing on instead is ensuring Northern Ireland's voice is heard in the negotiations with the EU. The First Minister, however, will be ensuring that happens."