Ireland’s Government has “confirmed” there will be no Irish police deployed to the border on the island, the Northern Ireland Office (NIO) said.

The Northern Ireland Secretary and the Irish deputy prime minister held a phone call on Wednesday evening amid diplomatic tensions after Dublin said there had been an upsurge in asylum seekers crossing the border following the passing of the UK’s Safety of Rwanda Act.

Concern was raised after Irish justice minister Helen McEntee said her department was planning to make 100 additional police officers available for “frontline enforcement work”.

While Dublin insisted they would not be “assigned to physically police the border with Northern Ireland”, Prime Minister Rishi Sunak told the Commons he wanted “urgent clarification” that there would be no disruption or checkpoints near the border.

In a statement later on Wednesday, the NIO said Northern Ireland Secretary Christ Heaton-Harris had a “constructive phone call” about illegal migration with Irish deputy premier (Tanaiste) Micheal Martin.

It said: “The Tanaiste confirmed that there will be no deployment of officers from An Garda Siochana (Irish police) to the Northern Ireland/Ireland border and that the Irish Government shared a steadfast commitment to securing the external border of the Common Travel Area.”

Another focal point of the diplomatic row centred on Dublin passing emergency legislation to deem the UK as a “safe country” for the return of asylum seekers.

Both governments have acknowledged the existence of an “operational agreement” which provides for the reciprocal return of asylum seekers between the UK and Ireland, but Downing Street has said it contains no legal obligations to accept them.

The Prime Minister said he was “not interested” in a returns deal if the European Union did not allow the UK to send back asylum seekers who had crossed the English Channel from France.

In a softening of language, the statement from the NIO on Wednesday concluded: “The Secretary of State reiterated that the UK will not accept any readmissions or returns arrangements that are not in our interest.”

The phone call came after Mr Sunak said the Irish Government “must uphold its promises” to avoid a hard border on the island of Ireland and avoid setting up checkpoints to prevent asylum seekers entering the country.

Answering questions in the Commons, Mr Sunak said 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.”

The Prime Minister was replying to a question from DUP MP Carla Lockhart, who accused the Irish Government of “hypocrisy” given its stance on the border during Brexit negotiations.

Asked about Mr Sunak’s comments, Irish premier Simon Harris reiterated that no gardai (Irish police) will be sent to border areas, saying: “Of course there won’t be.”

Noting upcoming elections in the UK, he expressed a desire to not become “involved in the day-to-day back and forth in the House of Commons”.

However, he stressed the “importance of countries upholding agreements”.

Mr Harris said: “We’ll uphold the agreement we have with Britain under the common travel area, the standard operating procedure that we have in place.

“I also welcome the comments of the Northern Ireland Secretary of State, where he referred to the importance of the two countries working together to protect the common travel area from abuses.

“Regularising our laws in relation to the arrangement we have with Britain is only one of a number of things we intend to do to ensure we have a firm, effective migration system.”

Asked about the diplomatic dispute, Sinn Fein leader Mary Lou McDonald said Mr Harris had provided Mr Sunak’s Government with a “propaganda coup” in the run-up to elections.

Speaking to Irish national broadcaster RTE, she added: “It’s never a good place for the Irish Government to be scoffed and laughed at in the House of Commons.”

Downing Street 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.

Labour said it agreed with the Government that the UK should not accept returns from Ireland “while Britain is not able to return people who arrive here from the EU”.

Mr Martin has previously said a figure provided by Irish justice minister Helen McEntee that approximately 80% of asylum seekers were coming from Northern Ireland was not “evidence-based” while DUP MP Ian Paisley told the Commons it was “made up”.

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.

It is not clear how many asylum seekers have crossed from Northern Ireland into the Republic, with Downing Street saying it did not have that data as the border is not policed.