Prime Minister Boris Johnson and his Irish counterpart Leo Varadkar agree they can "see a pathway to a possible deal" after talks, Downing Street says.
The leaders spoke for over two hours, including a one-to-one discussion during a walk in the grounds of Thornton Manor in north-west England.
Mr Varadkar said Thursday's "positive" meeting was "sufficient to allow negotiations to resume in Brussels".
Brexit Secretary Stephen Barclay will meet the EU's Michel Barnier on Friday.