Brexit Secretary David Davis said he had a "constructive and amicable" meeting with his counterparts from the devolved administrations, as the Scottish Brexit Minister urged the UK Government to provide "greater clarity and transparency" on plans to leave the EU.
Mr Davis laid out plans for the UK Government to hold monthly meetings of the EU Negotiation Joint Ministerial Committee, enabling the Scottish Government, the Welsh Government and the Northern Ireland Executive to share analysis as part of a "two-way information flow".
Mr Davis said the moves will allow the devolved administrations to voice their views as the Government prepares for divorce talks with Brussels which he insists will still be launched by next April, despite the High Court ruling that Parliament, and not Prime Minister Theresa May, must trigger that process.
Following the meeting on Wednesday, Scottish Brexit Minister Mike Russell said: "Although it is good that the process of involving the Scottish Government and the other devolved administrations is under way, more than four months after the referendum the UK Government has still not made its strategic intentions clear.
"There was a discussion over EU market access but we do not know whether UK ministers want to remain inside the single market or the customs union. This will remain a considerable problem as we continue to promote the interests of Scotland.
"The UK Government must provide greater clarity and transparency on its intentions."
He said he made it "absolutely clear" that membership of the single market "is essential for the economic prosperity of Scotland".
Mr Davis said: "Today's meeting was an important step in bringing the devolved administrations together with the UK Government to discuss how we can work together to get the best deal for the whole of the UK.
"Naturally, there are different standpoints around the table, but the meeting was constructive and amicable. We will meet regularly and share our latest thinking as the UK shapes its negotiating strategy.
'We will work positively with the Scottish Government, the Welsh Government and the Northern Ireland Executive as we implement the decision of the people of the UK to leave the EU."
The UK Government hopes the High Court judgment on how Article 50 will be triggered will be overruled on appeal to the Supreme Court next month.
Scotland's First Minister Nicola Sturgeon said Edinburgh would be seeking to intervene against the UK Government in its attempt to overturn the High Court ruling, saying she was not trying to veto the right of England and Wales to withdraw from the EU, but insisted the large majority of Scottish voters who backed Remain could not be "brushed aside as if they do not matter".
The First Minister said Scotland's most senior law officer, the Lord Advocate James Wolffe, would lodge an application to intervene in the legal case.
Meanwhile, Northern Ireland's First and Deputy First Ministers pledged to "take every opportunity" to highlight the region's unique situation during the negotiations.
In a joint statement, Arlene Foster and Martin McGuinness insisted they were united on the issue.
"Our attendance today sends out a clear signal that we are determined to work together to champion the interests of the people we represent," the ministers said.
"We have received assurances from the Prime Minister down that the Northern Ireland Executive will be fully represented in the negotiating process. We will ensure that those promises are honoured.
"We will continue to take every opportunity to re-iterate our agreed priorities and to emphasise the unique nature of our situation.
Meanwhile, Northern Ireland Secretary James Brokenshire also described the meeting as useful and said there was a "clear work programme in place".
He said: "Today's meeting was a constructive session in looking at how the devolved administrations work with one another and at how we can share our analysis to inform the evidence base we're putting together."
Brexit was also expected to be high on the agenda as Mrs May held talks in Downing Street with her Hungarian counterpart Viktor Orban.
During her meeting with Mr Orban, Mrs May reiterated her commitment to triggering Article 50 to begin Brexit by April despite the High Court ruling, Downing Street said.
She also reaffirmed that she "wants and expects" to protect the rights of EU nationals in the UK, as long as British citizens' living in Europe are protected in return, a spokesman said.
And the PM told Mr Orban, who has failed in his attempt to block the settlement of refugees to Hungary in an EU-set quota scheme, that refugees should be hosted in the first safe country they travel to and that "all states have the rights and responsibilities to control their borders and accept returned illegal migrants".