Boris Johnson has been told by Leo Varadkar that the EU remains “united” in its view that it will not renegotiate the Brexit deal.
The prime minister clashed with his Irish counterpart over the backstop in their first phone call since he took office.
Johnson told the Taoiseach that he will approach Brexit negotiations in “a spirit of friendship”.
Downing Street said he reiterated that any fresh deal must see the backstop abolished.
But the Irish government said Varadkar told Johnson that the emergency measure to prevent a hard border on the island was “necessary as a consequence” of UK decisions.
The call on Tuesday came after the pound fell to a two-year low as Johnson’s new government hardened its tone over the likelihood of a no-deal.
Their first discussion, nearly a week since Johnson became PM, also came after allegations that the PM was snubbing the Taoiseach.
No.10′s account of the call said Johnson warned that the UK will be leaving the European Union by the October 31 deadline “no matter what”.
But Johnson reaffirmed his commitment to upholding the Good Friday Agreement and to “never put” physical checks or infrastructure on the border, according to a spokeswoman.
“The prime minister made clear that the Government will approach any negotiations which take place with determination and energy, and in a spirit of friendship, and that his clear preference is to leave the EU with a deal, but it must be one that abolishes the backstop,” she added.
Dublin said Varadkar reiterated the EU position that Theresa May’s Withdrawal Agreement would not be renegotiated.
“On Brexit, the Taoiseach emphasised to the prime minister that the backstop was necessary as a consequence of decisions taken in the UK and by the UK Government,” a spokesman said.
“Alternative arrangements could replace the backstop in the future, as envisaged in the Withdrawal Agreement and the Political Declaration on the future relationship, but thus far satisfactory options have yet to be identified and demonstrated.”
The Taoiseach also invited Johnson to Dublin to “further their respective analyses on Brexit”, Ireland said.
But the PM has so far refused to sit down with EU leaders until they agree to renegotiate the Withdrawal Agreement.
That deal failed to win the approval of parliament three times, despite Johnson once voting for it.
A key sticking point has been the backstop, a last resort to prevent a much-feared hard border on the island if no all-encompassing deal can be agreed between the UK and the bloc.