The Irish Refugee Council has said there will be a further increase of migrants in the months and years ahead.
Its Chief Executive Sue Conlon said this is in line with the trends being seen in other countries.
However, she said that if reports of hundreds arriving in Ireland in recent months are accurate, then this would be higher than her organisation has previously been told.
Ms Conlan was responding to reports that the Justice Minister has expressed concern to the Cabinet that increased immigration in recent months has the potential to increase pressure on immigration and public services.
She said she is unsure if these figures are accurate or speculation and they can only be verified by state authorities concerned.
Ms Conlon said one of the issues this raises is the lack of transparency and clarity in the immigration system in Ireland.
She said that if there were clearer categories and clearer regulations that had to be met the asylum process might not be abused.
Call to tackle migrants using trucks
Earlier, the Irish Road Haulage Association called on the Government to liaise with the British government to take the onus of responsibility for carrying migrants from truck drivers.
It comes after large numbers of migrants in the port of Calais in France attempted to board vehicles bound for Britain yesterday.
Speaking on RTÉ's Today with Sean O'Rourke, IRHA President Eoin Gavin said the problem was that the port of Calais was unsecure, with no barriers or security.
Mr Gavin said if a truck driver is found with migrants on board in Britain, they are held responsible.
He said making a criminal out of the driver is leading them to take extraordinary measures in trying to get people hiding out of their vehicles.
He said lives will be lost if the situation is not addressed.
Mr Gavin said the IRHA has been in touch with the Department of Transport and the Department of Foreign Affairs on this issue.
He said the British government was putting pressure on Irish truck drivers and other European drivers to be border control officials.
Mr Gavin said Irish truck drivers were having to contend with very difficult conditions and described one incident involving an Irish truck driver aged in his 70s.
"We had a driver down as far as Bordeaux, which is 14 hours driving away from Calais, with a refrigerated unit where he went to do his vehicle check in the morning and discovered there were people inside the fridge.
"The security guard in the truck park where he was parked and himself came under attack from these 'clandestines', who were armed with knives and iron bars", Mr Gavin said.
He reiterated that drivers should not feel that they are going to be treated like criminals if migrants have managed to conceal themselves on board their vehicles.
Meanwhile, services through the Channel Tunnel between England and France are returning to normal after a day of disruption by striking French ferry workers yesterday.
The tunnel had to be shut yesterday when the workers broke in and migrants attempted to board UK-bound lorries.
Migrants were seen at the side of the motorway in Calais while others were seen opening the back doors on lorries stuck in traffic.