LONDON — The Taoiseach (Irish prime minister) Simon Harris has said foreign migration policies "cannot be allowed to undermine ours".
He added Ireland will "not provide a loophole for anybody else's migration challenges".
Harris has asked Justice Minister Helen McEntee to bring legislation to Cabinet on Tuesday to enable asylum seekers to be sent back to the UK.
On Tuesday, McEntee said 80% of recent arrivals to the Republic came from the UK across the Irish border.
Legislation to revive the UK's Rwanda policy became law on Thursday.
It aims to deter people from crossing the English Channel by sending some asylum seekers to the central African country.
No migrants have yet been sent from the UK.
The UK government had hoped for flights to take off by the spring but Prime Minister Rishi Sunak said this should now happen within 10 to 12 weeks.
On Sunday, Harris attended a memorial event in County Monaghan to mark 50 years since the death of Fine Gael Senator Billy Fox, the only Oireachtas (parliament) member to be killed during the Troubles.
When questioned on migration, the taoiseach said he doesn't intend to allow foreign policies to "affect the integrity of our own".
"This country will not in any way shape or form provide a loophole for anybody else's migration challenges - that's very clear," he told reporters.
"From an Irish perspective we intend to have a firm, rules-based system, where rules are in place, where rules are enforced and where rules are seen to be enforced.
"Anybody else's migration policy can’t be allowed to undermine ours."
Harris said there had previously been a returns agreement in place between Ireland the UK.
This agreement is now set to be updated when McEntee brings forward legislative proposals next week.
"It’s one which will effectively allow people to be returned to the United Kingdom," he said. "I think that’s quite appropriate."
The taoiseach added that while the Police Service of Northern Ireland (PSNI) and An Garda Síochána (Irish police force) already collaborate on migration, there is now "a need for much more of that".
Speaking on RTÉ's Six One News on Saturday, McEntee said: "There are many reasons why we have seen an increase in migration toward Ireland.
"What's clear in the decision that the UK have taken in choosing Brexit, they have actually seen an increase in people seeking asylum in their country. The way that they deal with that, it's their policy.
"My focus as minister for justice is making sure that we have an effective immigration structure and system.
"That's why I'm introducing fast processing. That's why I'll have emergency legislation at Cabinet this week to make sure that we can effectively return people to the UK and that's why I'll be meeting with the home secretary [James Cleverly] to raise these issues on Monday."
Earlier in the week, McEntee told a committee of the Oireachtas there had been a rise in the number of people crossing the land border between Northern Ireland and the Republic, with this now making up 80% of the total number of asylum seekers.
In response to her comments, McEntee said the UK government's Rwanda policy meant people were "fearful" of staying in the UK and were crossing the border to the Republic so they would not be sent to Rwanda. Martin, who also serves as Ireland's foreign minister, has spoken of his opposition to the policy.
On Sky News on Sunday, Prime Minister Rishi Sunak was asked whether Martin's comments showed the UK was "exporting the problem".
Sunak replied: "The deterrent is — according to your comment — already having an impact, because people are worried about coming here and that demonstrates exactly what I'm saying: if people come to our country illegally, but know that they won't be able to stay, they're much less likely to come."
It comes as Home Office figures showed some 500 migrants had crossed the English Channel over two days — with 141 people arriving on Friday and 359 on Saturday, in a total of 10 small boats.
It brings the number of arrivals on small boats to 7,167 so far this year, which is higher compared to the same period the year before.
Sunak told Sky News that illegal migration was a "global problem" and said many countries were looking to replicate "third-country partnerships" similar to the agreement struck between the UK and Rwanda.
A No 10 spokesperson had previously said it was "too early to jump to specific conclusions about the impact of the act and treaty in terms of migrant behavior".
The Safety of Rwanda Act, which aims to avoid further legal challenges to the policy by declaring Rwanda a safe country, was approved by MPs and peers this week and passed into law on Thursday — although the plan could still be held up by court challenges. — BBC