Concern was raised at a private Fine Gael meeting over asylum seekers losing or destroying passports while flying into the State.
Minister of State Patrick O’Donovan raised the issue of undocumented arrivals at Wednesday’s parliamentary party meeting.
Sources said he told the meeting that the level of fines that can be imposed on airlines over the issue are “far too low”.
The Government has sanctioned the resumption of passport checks at the steps of aircraft in an attempt to address the significant numbers of asylum seekers who have lost or destroyed their travel documents while flying into the State.
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The move was prompted by figures showing that 40 per cent, or more than 5,000 people, who applied for international protection last year either lost or destroyed their travel documents before arriving at Irish immigration control.
Mr O’Donovan was also among a number of participants at Wednesday’s Fine Gael meeting that said that communities around the country have concerns about the impact of the increased immigration being experienced on access to services.
Limerick County TD Mr O’Donovan said the “vast majority” or people are in that category and not all protesters are far right or trouble-makers.
Mayo TD Michael Ring is understood to have raised concerns about access to health services and Senator Paddy Burke made a similar contribution on community issues.
Mr Ring told the meeting he’s “not far right or far left”, that he’s “down the middle” and communities have concerns over a lack of information.
Minister for Justice Simon Harris is said to have told TDs and Senators that Ireland has “a rules-based system” and it is important that it is “fair and efficient”.
He outlined measures being tackle to strengthen Ireland’s international protection regime including a resumption in deportation orders - which had stopped during the pandemic” and efforts to ensure faster turn-around times for the applications of asylum seekers from so-called safe countries.
Sources said Mr Harris also told the meeting there is “a world of difference” between people in communities raising questions and looking for information and “thuggish behaviour” at some protests.
Taoiseach Leo Varadkar said that migration into the EU will be discussed at this week’s European Council meeting.
He said all EU countries face challenges with large numbers of people entering the EU last year as refugees or to seek international protection.
He said there was a need to ensure people who need protection get it while also better securing Europe’s external borders to stop human trafficking and work with third countries to increase returns.
Mr Varadkar said it was important the issue was handled “sensitively, factually and appropriately”.
He said the Russian war on Ukraine and EU economic affairs are also on the agenda of the European summit.
He also spoke about Attorney General Rossa Fanning’s report on the legal strategy by successive governments in response to claims arising from nursing home charges and the non-payment of Disabled Persons’ Maintenance Allowance.
He said Government will do whatever is legally required, just and in the public interest.
Mr Varadkar described the Attorney General’s report as “very solid” and said it is “is worth reading to get a good handle on the issue”.
Earlier on Wednesday Labour leader Ivana Bacik said Mr Fanning’s report misses an “overall pattern” in the treatment of people denied their legal rights, arguing it fails to take into account the moral duty of the State to its citizens.
She told RTÉ's Morning Ireland that there should be a redress scheme for people impacted, arguing that the report conflated the “narrow interest of the Government with what is in the public interest”.
