Taoiseach Leo Varadkar and UK Prime Minister Boris Johnson spoke on the phone for almost an hour this evening.
The leaders shared perspectives on the Withdrawal Agreement, with Mr Johnson indicating it will not get through the House Commons.
Mr Johnson said the backstop would need to be removed and that an alternative solution is required.
The Taoiseach reiterated the EU27 position that the Withdrawal Agreement cannot be reopened.
Mr Varadkar also emphasised the importance of "the legally operable guarantee to ensure no hard border and continued free trade on the island of Ireland," according to the Government Press Office.
Mr Johnson made it clear that the Common Travel Area would not be effected by the ending of freedom of movement after Brexit.
Both the Taoiseach and Mr Johnson reiterated their desire to see the Northern Ireland political institutions reinstated urgently and agreed to work closely to this end.
Both leaders condemned the bombing in Fermanagh earlier this morning.
Mr Varadkar and Mr Johnson agreed to meet in Dublin in early September.