Some 50 asylum seekers trying to enter the Republic of Ireland were returned to the UK last week, according to Barry Cowen.
Gardaí said these people were found to have entered Ireland illegally and were refused "leave to land" as part of Operation Sonnet.
Deputy Cowen said the additional resources for the Garda National Immigration Bureau (GNIB) are welcome – but not enough.
“I have been calling for increased resources for GNIB to allow them to adequately police and perform immigration checks along the border and indeed throughout the country,” he said.
“Fast, firm and fair deportations of illegal migrants resulting from a coordinated effort by GNIB and Department of Justice is exactly what I have been calling for.”
Cowen calls for 'meaningful impact'
According to Deputy Cowen, Operation Sonnet is now being deployed weekly and will aim to have 100 members by the end of 2024.
“That is not enough,” he said. “We can see the meaningful impact this unit has had in just one week.
“Year’s end is simply too far away - illegal immigration is a real issue and one that needs to be tackled now.
“I am calling for daily checks by Operation Sonnet and significant resources for members working from GNIB immediately.
“Their efforts are clearly successful and must be ramped up further to stem the flow of illegal migrants from the UK.”
'We're not a soft touch'
Mr Cowen, Fianna Fáil's election candidate for the Midlands Northwest said Irish people have always welcomed ‘legitimate’ immigrants seeking asylum, but don’t want to be taken advantage of.
“20% of the workforce currently being non-Irish [is] making a contribution and we are better for [them],” he told Newstalk.
“But decent hardworking citizens just want to see that we’re not being seen as just a soft touch, we’re not being taken for a ride.”
This follows comments by UK Prime Minister Rishi Sunak in April that his Rwanda policy is working, based on the number of asylum seekers coming into the Republic from Northern Ireland.
Taoiseach Simon Harris later said Ireland will not provide a "loophole" for other countries' migration challenges.
According to Gardaí, 107 were detected entering the State without the requisite visas or identity documents so far this year.
