Brosnan and his bride married in County Mayo on 4 August
On Thursday the paper published a set of photographs which Hello! billed in this week's issue as world exclusives.
The Irish Star is 50% owned by Richard Desmond, the proprietor of OK! Magazine, a rival to Hello!
If a settlement is not reached, legal action is likely to commence within the next week, according to magazine's solicitors Charles Russell.
The Irish Star was unavailable for comment.
'Seven-figure sum'
Mr Hall told BBC News Online of his reaction at seeing the photographs in the Irish Star.
"We were very, very angry," he said.
"We spent six months negotiating the rights and they cost us a seven-figure sum.
"I asked the editor of the Irish Star how he got the pictures and he said he didn't know - that's ridiculous."
Chris Hutchings, solicitor for Hello! at Charles Russell told BBC News Online: "No negatives were supplied by our clients.
"One can assume that the pictures were scanned - but that's speculative at this stage."
Mr Hall dismissed the suggestion that anyone at Hello! might have been involved in scooping the exclusive.
"There's no way this could be an inside job - the photos were marshalled by a security officer at all times."
'Compensation'
Mr Hutchings said that the magazine would be pressing for a substantial settlement.
"I can't divulge the amount, but it was a very valuable feature and a very substantial sum was paid, and they will be looking for an appropriate sum of compensation for spoiling the exclusive," said Mr Hutchings.
In 2000, OK! obtained an injunction against Hello! after the latter bought photographs of the wedding of Michael Douglas to Catherine Zeta Jones, to which OK! had obtained the exclusive rights.
Mr Hutchings said that if the Irish Star did not respond, legal action could follow swiftly.
"They've had a letter of complaint, but we haven't heard back yet," he said.
"If we don't have a satisfactory response with undertakings, legal action will be commenced in the next week."