A Downing Street spokesperson said:
The Taoiseach congratulated the Prime Minister on his appointment and both leaders underscored their commitment to working closely together in the spirit of the warm and deep relationship between the UK and Ireland.
On the process of restoring the Executive and Assembly in Northern Ireland, both leaders expressed their determination to see this happen as quickly as possible.
The Prime Minister said the ongoing talks have his unequivocal support and that he wanted to continue to work closely with the Irish government to help drive the process towards a successful conclusion. He said he looked forward to visiting Northern Ireland shortly and talking to the leaders of the five main parties about this.
On Brexit, the Prime Minister made clear that the UK will be leaving the EU on October 31, no matter what.
He said that in all scenarios, the Government will be steadfast in its commitment to the Belfast Agreement and will never put physical checks or physical infrastructure on the border.
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.
The two leaders agreed to stay in contact.