Taoiseach Simon Harris has said there will not be a garda presence at the border to prevent asylum seekers crossing from Northern Ireland to the Republic.
He was speaking after British Prime Minister Rishi Sunak sought "clarification" on the issue and said the Irish Government "must uphold its promises" to avoid a hard border.
Mr Sunak also said the UK has no legal obligation to accept returns of illegal migrants from Ireland.
Yesterday, the Government said it would draft emergency legislation to designate the UK as a safe country, allowing Ireland to return asylum seekers.
It also said that 100 gardaí would be made available for frontline immigration enforcement duties, although it insisted they would not be "assigned to physically police the border with Northern Ireland".
Mr Harris pledged that Ireland would uphold its agreement with Britain under the Common Travel Area which he described as the "standard operating procedure".
Earlier, Mr Sunak told the House of Commons that ministers were seeking "urgent clarification that there will be no disruption or police checkpoints at or near the border" and that there must not be "cherry-picking of important international agreements".
He added: "Now, it's no surprise that our robust approach to illegal migration is providing a deterrent but the answer is not sending police to villages in Donegal. It's to work with us in partnership to strengthen our external borders all around the Common Travel Area that we share."
Mr Sunak's comments came in response to a question from Democratic Unionist Party MP Carla Lockhart, who accused the British government of "hypocrisy" given its stance on the border during Brexit negotiations.
Diplomatic tensions between London and Dublin have increased in recent days after Minister for Justice Helen McEntee claimed there had been an upsurge in asylum seekers crossing the border following the passing of the UK's Safety of Rwanda Act.
The British government has repeatedly stressed that the UK is under no legal obligation to accept returns of asylum seekers from Ireland, and would not do so while France continued to refuse to accept returns from the UK.
There is an operational agreement on the Common Travel Area which Ireland says provides for returning asylum seekers, but Mr Sunak's spokesman said this was not legally binding and nobody had been returned to the UK under its terms.
One person has been sent back to Ireland under the agreement since it was signed four years ago, the spokesman added.
The UK government has claimed the reported increase in asylum seekers entering Ireland from Northern Ireland demonstrated that its Rwanda scheme was already acting as a deterrent.
How the Common Travel Area impacts migration
The Taoiseach said that he would not get involved in British politics, ahead of local elections tomorrow, adding that he had no interest in "back and forths" in the House of Commons.
"But what I do have is an interest in is agreements ... and I very much welcome the British prime minister's comments in relation to upholding agreements," Mr Harris said.
"We’ll uphold the agreement that we have with Britain under the Common Travel Area - the standard operating procedure we have in place."
Mr Harris had previously said that Ireland will not "provide a loophole" for other countries' migration "challenges".
It is not clear how many asylum seekers have crossed the border into Ireland.
Tánaiste Micheál Martin said Ms McEntee's figure of 80% of total border crossings was not "evidence-based", but based on presentations, while DUP MP Ian Paisley told the Commons it was "made up".
The British government said it did not have data on crossings as the border is not policed.
Earlier, Mr Harris told the Dáil that has been "a very significant increase in deportations" recently, which has seen "173 people depart this State under various mechanisms up to 26 April".
He was responding to Aontú leader Peadar Tóibín who said the Minister of Justice is failing to establish basic information about asylum seekers, calling this "a flashing neon light of incompetency".
"Shockingly we have this crisis on our hands," the deputy said, "largely because the Minister for Justice does not know what is happening in the department".
He detailed various statistics he sought from the Department of Justice relating to asylum seekers which it was unable to provide, including the number of people against whom deportation orders have been issued and who have left the State.
Ms McEntee's failings have led to an increase in the numbers entering Ireland and a breakdown with relations with the UK, Mr Tóibín claimed.
The Taoiseach rejected the "hypothesis" and said migration numbers were not caused by any minister for justice.
"If you can't measure what is happening, you can't manage the situation," Mr Tóibín responded.
Sinn Féin leader Mary Lou McDonald repeated her claim today that the Government has displayed incompetence and offered a "gift to the Tories" in its approach to migration and returns to the UK.
Speaking on RTÉ's Six One, Ms McDonald said there has been "confusion and chaos" over the issue in recent days.
"It's never a good place for the Irish Government to be scoffed and laughed at in the House of Commons," she said.
Ms McDonald suggested that there needs to be a legal remedy and a diplomatic fix between Ireland and the UK.
"We need a Government that's very surefooted in brokering that. What we have seen over the last number of days has been confusion and chaos where we needed calm and clarity."
Martin wants 'Covid style response' to immigration
The Tánaiste has told a meeting of the Fianna Fail parliamentary party that communication and engagement on the immigration issue must improve on all fronts.
Micheál Martin said he wants to see a Covid-19 style response, adding that the numbers of people claiming asylum have increased considerably over the past 18-24 months, creating significant challenges for the State.
He said that political slogans or promises will not solve the issue and further cooperation on an international level is the only solution.
"We also need to strengthen procedures and processes," Mr Martin said.
Cork East Fianna Fáil TD James O’Connor told the meeting that it was time to have a serious conversation about Ministers Helen McEntee and Roderic O’Gorman.
He was particularly critical of Ms McEntee’s performance at the Oireachtas Committee on Justice and cited the public’s concern at the handling of migration and how it is affecting Fianna Fáil’s support.
Additional reporting Mícheál Lehane
