Scotland First Minister Nicola Sturgeon and Welsh First Minister Carwyn Jones were in the Welsh capital for a meeting of the British Irish Council. Other people at the meeting included Ireland's Prime Minister Enda Kenny, Xinhua news agency reported.
During talks after the British Irish Council Summit, Sturgeon and Jones also discussed ways in which the ambitions of Scotland and Wales can be fulfilled.
Sturgeon has made it clear that if a Brexit deal is not suitable for Scotland she will bid for a second referendum to sever Scotland's ties with Britain.
Speaking after the meeting, Sturgeon said Friday's meeting was another positive and useful opportunity to discuss some of the shared concerns both Scotland and Wales have around Britain's exit from the European Union.
"Both Scotland and Wales have spoken loud and clear -- Single Market status is simply the only way to protect the economy not only of Scotland and Wales respectively, but the UK as a whole. Anything else risks us falling off a hard-Brexit cliff edge, and we are united in our call to ensure the UK Government does all it can to ensure that happens."
Carwyn Jones said:" This has been a constructive discussion where we have shared our very strong concerns over the prospect of Britain's pursuing a hard Brexit."
"We will continue to work together to build a coalition in favour of Britain having full and unfettered access to the single market," he said.
There was criticism in Cardiff that Britain's Prime Minister Theresa May had not attended the summit meeting.
Although a number of British government ministers attended the event, Sturgeon and Northern Ireland's Deputy First Minister Martin McGuinness both said May should have attended the British Irish Council (BIC) meeting in Wales.
Northern Ireland Secretary James Brokenshire, who did attend the talks said: "The Prime Minister strongly supports the British Irish Council," adding that is why two British government cabinet ministers and two other government ministers attended the Cardiff meeting strongly representing the British government's perspective.
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