The prime minister and the taoiseach (Irish prime minister) have “shared perspectives on the withdrawal agreement” in a phone conversation.
Boris Johnson and Leo Varadkar spoke for almost an hour on Monday evening, the two governments said.
Mr Johnson said the agreement in its current form would not get through the House of Commons, while Mr Varadkar reiterated that it cannot be reopened.
Both prime ministers condemned Monday’s bomb in County Fermanagh.
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The phone call comes a day after a government dossier warning of the impact of a no-deal Brexit was leaked.
The report said leaving the EU without a deal could lead to a hard Irish border after plans to avoid checks fail.
Mr Johnson maintained that the “backstop would need to be removed”, while Mr Varadkar “emphasised the importance of the legally operable guarantee to ensure no hard border and continued free trade on the island of Ireland”.
The backstop, part of the withdrawal agreement negotiated by former prime minster Theresa May, is an insurance policy to prevent a hard border returning on the island of Ireland, which if implemented, would see Northern Ireland staying aligned to some rules of the EU single market.
It would also involve a temporary single customs territory, effectively keeping the whole of the UK in the EU customs union. These arrangements would apply unless and until both the EU and UK agreed they were no longer necessary.
The prime ministers also spoke about the need for the power-sharing executive at Stormont to be reinstated and “agreed to work closely to this end”.
The leaders also agreed to meet face to face in Dublin in early September.
Brexit: Johnson and Varadkar in hour-long call}