More than 1,000 people have offered loving homes to the 116 puppies found crammed into two vans at Dublin Port.
They contacted the Dublin Society for the Prevention of Cruelty to Animals (DSPCA) after the charity took the pups into its care on Wednesday night.
"We've had over 1,000 calls and emails for the public so far," said DSPCA spokeswoman Gillian Bird. "We've also had support from Minister for Agriculture Simon Coveney who is taking an interest."
The puppies were found "crammed" into the vans that were part of a shipment bound for the UK.
They were seized because officials beleived there was a lack of water and food for the animals for their journey to Britain and there was no paperwork or "puppy passports".
These breaches of the new animal welfare laws prompted the seizure, said Ms Bird.
"A judge will decide the matter when the evidence is heard which, hopefully, will be within the next week," she said. "In the meantime, many of pups will be put into foster care with registered individuals."
This was the first case of its type under the new Animal Health and Welfare Act 2013.
The DSPCA is authorised to pursue prosecutions in such matters. No charges have yet been made against any individuals, but cautions have been issued.
Sources said it was "probable" that some of the animals would have died en route to Britain because they were crammed so close together. Thirty-two needed veterinary care.
A Department of Agriculture spokeswoman said Mr Coveney met DSPCA officials on Wednesday along with members of the EU-wide Eurogroup, which campaigns for effective animal safety legislation.
The minister acknowledged the ongoing cooperation between his department, An Garda Siochana, Customs, the DSPCA and other animal welfare bodies.
"I welcome the action taken by the authorities and the DSPCA. We must remain vigilant and maintain the highest standards and ensure strict enforcement of the Animal Welfare Legislation," said Mr Coveney.
A man in his 40s, a resident of Co Cavan, was questioned by customs officers about the seized puppies.
Two middle-aged men from Co Carlow and Co Armagh were also questioned.
The seized puppies included pugs, huskies, cockers, Yorkshire terriers and designer breeds such as Cavachons and labradoodles.
Some were as young as four weeks, according to the DSPCA veterinary team.