Carwyn Jones was speaking after a meeting in Cardiff Friday of the British Irish Council. The extraordinary meeting of the council took place in the Welsh capital to discuss the decision by Briton's in the June 23 referendum to leave the EU.
As well as the Westminster-based British parliament, Jones wants the Scottish and Welsh parliaments as well as the Northern Ireland Assembly to be involved in the Brexit decision making.
Jones said: "Any future deal the UK agrees should be ratified by all four parliaments in order to get greatest buy-in."
Scotland's First Minister Nicola Sturgeon, Northern Ireland First Minister Arlene Foster and deputy First Minister Martin McGuinness were at the council meeting, along with Prime Minister of the Irish Republic Enda Kenny and representatives of the governments of the Isle of Man, and the islands of Jersey and Guernsey. The British government delegation was led by Alun Cairns, Secretary of State for Wales, and Northern Ireland Secretary James Brokenshire MP.
Sturgeon described the emergency meeting as one of the most important ever for the council, coming in the aftermath of Britain's vote to leave the EU.
The SNP politician has pledged to protect Scotland's links with the EU. In the referendum Scottish voters voted to remain in the EU by a margin of 62 percent to 38 percent.
Sturgeon said Friday in Cardiff: "Scotland voted overwhelming to remain within the European Union and that democratic choice by the Scottish people will guide us as we seek to maintain our relationship with the EU."
Last week Sturgeon held a meeting in Edinburgh with British Prime Minister Theresa May to discuss Scotland's response to the Brexit vote.
Jones said he called the special session of the council to discuss the implications of the Brexit vote, including how EU funding will be replaced. He also wanted council members to discuss the question of the border between Northern Ireland and the Irish Republic.
Currently there is no land border between the two parts of the island of Ireland, but once Britain leaves the EU, the Irish border will become a border of the EU.
Speaking at a news conference after the meeting, on Friday, Jones said the three devolved governments should need to give permission before the formal process of Brexit begins.
Jones said there would be "fundamental changes" as a result of the EU referendum, adding: "During this tumultuous time, it is more important than ever to maintain the strength of this relationship and work together to map out a successful way forward."
In an official communique, the council said later: "The council noted that there are a number of priority areas where implications arise, in particular: the economy and trade, the Common Travel Area (which allows the free movement of people and goods between Britain and the Irish Republic), relations with the EU and the status of all citizens affected by the change.
"During discussions, ministers collectively reaffirmed the importance of the Council as a key institution and an important and unique forum to share views, enhance cooperation and strengthen relationships. They reiterated their commitment to facilitating harmonious and mutually beneficial relationships among the people of these islands."
At the meeting Northern Ireland Brokenshire repeated prime minister Theresa May's message that "Brexit means Brexit", adding that May's new Conservative administration was "in a listening mode".
The council will meet again in November, also in Cardiff.