British Prime Minister Boris Johnson and his Irish counterpart Leo Varadkar said they could see a route towards striking a possible Brexit divorce deal, following a crunch meeting on Thursday.
"Both continue to believe a deal is in everybody's interest. They agreed that they could see a pathway to a possible deal," the pair said in a joint statement.
There are just days left to strike a deal. The agreement must be signed off at an October 17-18 EU summit and European officials want the negotiations to conclude in advance.
Britain is scheduled to leave the European Union on October 31, more than three years after triggering Brexit in a national referendum.
The key sticking point in the tortuous negotiations is the future arrangements on the currently invisible land border between the UK province of Northern Ireland and EU member the Republic of Ireland.
Johnson and Varadkar said they had "detailed and constructive" talks at a venue in Birkenhead, outside Liverpool in northwest England.
"Their discussions concentrated on the challenges of customs and consent," their statement said.
"They also discussed the potential to strengthen bilateral relations, including on Northern Ireland.
"They agreed to reflect further on their discussions and that officials would continue to engage intensively on them."
They said Varadkar would now consult with the EU task force, while Britain's Brexit Secretary Steve Barclay will meet with EU chief Brexit negotiator Michel Barnier on Friday.
Britain's pound sterling currency rose on the news, jumping up 0.5 percent against the dollar and 0.4 percent against the euro.
At around 1425 GMT, the pound was worth $1.2268, while a euro bought 89.83 pence.