Workplace inspections for migrants working illegally need to increase, the Taoiseach has said.
Simon Harris said there are a number of “common sense” changes to migration policy that need to be implemented in Ireland.
The Government has faced criticism for failing to accommodate all asylum seekers amid an increase in the number of arrivals.
There are more than 1,700 male international-protection applicants who have not yet received an offer of State-provided accommodation.
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In the last two weeks, the Government has directed multi-agency operations to clear large makeshift migrant encampments from Dublin city.
There have also been protests in towns and villages across the country over buildings being selected to house asylum seekers.
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A number of properties have also been severely damaged in suspected arson attacks.
Speaking on Monday, Mr Harris said that there was a need to be “honest” that Ireland can continue to provide shelter to asylum seekers but may not necessarily be able to provide housing.
He said: “Irish people are full of compassion, but you know what they’re also full of is common sense.
“And what they want to see when it comes to migration policy is compassion and common sense aligning.
“They want us to be honest to people coming to this country about what we can and can’t do.
“We can absolutely provide shelter but not necessarily housing for people who come here.”
The Taoiseach said Government “needs to do better” on accommodating asylum seekers through the use of State land as well as the provision of tents and sanitation facilities.
He also said there was a need to focus on faster processing times, “effective deportations”, and integrating people who have a right to remain in Ireland.
Speaking to Newstalk, Mr Harris said: “We need to look at welfare consistency, we need to look at a contribution that people who have status make to accommodation.
“We need to look at making sure that anybody in work is working legally, that there are more workplace inspections.
“There are a number of common-sense things we should do but crucially we need to work at a European level.”
Minister for Finance Michael McGrath said the Government was “learning as we go”, when it came to dealing with the large increases in asylum applicants in recent years.
Speaking on Monday, he said: “Ireland is not unique in trying to grapple with a very serious immigration challenge and we are responding in the best way we can.
“The numbers have continued to grow so the scale of the challenge is increasing all the time. And that’s why the response of the Irish Government has had to change as well,” Mr McGrath said.
“It is true that we are learning as we go as well, from the experience.
“The key focus now will be on ensuring faster processing of applications so that people who have legitimate entitlement to remain in Ireland get that decision quickly. But others who do not have a right to remain in the country that they get that decision and that that is executed as well quickly, so they can move on,” he said. – Additional reporting PA