Rishi Sunak said he was pleased with progress in the search for a resolution to the dispute on post-Brexit trade in Northern Ireland, after a British-Irish Council summit on Thursday.
The first UK prime minister to attend the summit for 15 years, he met the Irish Taoiseach Micheál Martin, who welcomed the extra time given to make progress in negotiations. Technical talks resumed recently after a seven-month break.
The summit was dominated by the Northern Ireland Protocol which regulates post-Brexit trading arrangements in the UK territory, where opposition from unionists means there is still no devolved government.
Both leaders tweeted positive messages about their discussions after the summit in Blackpool, northwest England.
"We all recognise that the protocol is having a real impact on the ground," Sunak told reporters.
"We had a very positive meeting, and what I want to do is find a negotiated solution, preferably," he said. "And I'm pleased with the progress that we're making in these early days in this job, and my focus is to try and find a resolution here."
The Irish prime minister said he welcomed that "time and space had been given to make progress" on the negotiations and allow for pragmatic operational solutions.
"People and businesses in Northern Ireland have been crystal clear that they want agreed solutions to the protocol issues and now is the time to do so," Micheál Martin said in a statement.
'We believe we can fix this', says UK minister
In recent weeks UK-Irish relations have warmed, and during Liz Truss's brief tenure in Downing Street there were reports of progress over the protocol -- negotiated before Brexit and part of the binding EU divorce deal -- which is at the root of the months-long political stalemate.
It's thought there may be some convergence over post-Brexit customs checks on goods shipped to Northern Ireland from other parts of the United Kingdom.
"We absolutely believe we can fix this by sharing of data," the UK's Northern Ireland Secretary Chris Heaton-Harris told LBC Radio earlier on Thursday.
The minister gave an indication of the government's resolve to break the deadlock when asked whether the protocol would still be talked about in six months' time. "God I hope not!" he replied.
The outgoing EU ambassador to the UK, João Vale de Almeida, told the Financial Times that the two sides were "not that far apart". The envoy also reportedly said that agreement could pave the way for the UK to rejoin the EU's Horizon Europe science programme.
Call for 'flexibility and pragmatism'
Sunak backed Brexit in the UK's 2016 referendum on leaving the EU -- but has struck a more emollient tone than Boris Johnson, who seemed to revel in provocation and fractious relations with the bloc.
However, the prime minister also backs the controversial Northern Ireland Protocol Bill, currently going through the British parliament, which would allow the government to rip up part of the Brexit divorce deal.
The legislation is a crucial issue for the influential anti-EU European Research Group (ERG) of Conservative MPs.
Other sticking points in the Brexit treaty include oversight by the European Court of Justice (ECJ) in Northern Ireland, which remains part of the EU single market for goods.
Rishi Sunak told his Irish counterpart at Thursday's summit that any deal must solve the full range of issues caused by the protocol but hoped for flexibility and pragmatism, according to a UK spokesman.
The British government has pushed back a deadline to hold a new election in Northern Ireland until at least March to provide space for progress in EU-UK talks on the protocol. Dublin and Brussels have signalled their hope to reach an agreement in the coming weeks.
At the summit, Rishi Sunak also met leaders of the UK's home countries of Scotland and Wales, who were snubbed by Truss during her tumultuous seven weeks in power. But there were no ministers from Northern Ireland because of the stalemate over the protocol.
Michelle O'Neill, leader of Irish nationalists Sinn Fein -- who is expected to become Northern Ireland's first minister if a government can be formed -- regretted on Twitter that there would be no Northern Ireland assembly representative in Blackpool because the unionist DUP party was "preventing our voices from being heard".
The British-Irish Council was established as part of Northern Ireland's 1998 "Good Friday" peace deal to promote cooperation between the Republic of Ireland and the United Kingdom.