Theresa May is holding high-level Brexit talks in Cardiff with Welsh First Minister Carwyn Jones and Scotland's Nicola Sturgeon on Monday (30 January).
The Joint Ministerial Committee is the first to take place outside of London and comes after the government tabled its Article 50 bill in parliament following a defeat at the Supreme Court.
"I know ministers and officials from all sides are also in regular contact bilaterally," May said.
"We have received papers from both the Scottish and Welsh governments and I am grateful to the devolved administrations for their contributions to this important process.
"We will not agree on everything, but that doesn't mean we will shy away from the necessary conversations and I hope we will have further constructive discussions."
The talks, which will include Brexit Secretary David Davis and International Trade Secretary Liam Fox, risk being overshadowed by the backlash against Donald Trump's travel ban.
The UK prime minister initially refused to condemn the initiative that blocks those from Iran, Iraq, Sudan, Syria, Yemen, Libya and Somalia from travelling to the US for 90 days.
Number 10 later said May "doesn't agree" with Trump's executive order.
Conservative MP Nadhim Zahawi, who was born in Iraq, spoke out against the clampdown on Sunday (29 January). "I don't think I have felt discriminated since little school when the kids were very cruel, as a young boy coming from Iraq of Kurdish origin," he told BBC One's Andrew Marr show.
Scottish Conservative leader Ruth Davidson and Labour leader Jeremy Corbyn were among the top politicians calling for Trump's state visit invitation to the UK to be revoked over the travel ban.
"After Trump's hideous actions and May's weak failure to condemn them, it's more important than ever for us to say to refugees seeking a place of safety that they will always be welcome in Britain," Corbyn said.
Hundreds of thousands of people have also signed an online petition in a bid to block the US president from travelling to Britain to meet The Queen in June. The petition author warned that Trump's audience with the monarch could cause her "embarrassment".
The row comes just days after May scored a diplomatic coup by becoming the first foreign leader to meet Trump in the White House. But the Conservative premier is now facing increasing pressure to distance herself from Trump's radical policies.
May is also expected to travel to Ireland to meet with Taoiseach Enda Kenny. Daniel Mulhall, Ireland ambassador to the UK, spoke to IBTimes UK on 13 January.