The Ministers met to discuss transport links between Northern Ireland and Scotland.
Speaking after the meeting in Edinburgh Mr Murphy, said: "Co-operation and communication at Ministerial level are important to maintaining and improving transport links between the North of Ireland and Scotland.
"The joint communiqué signed following the visit by Scottish First Minister, Alex Salmond, to the North of Ireland last year, contained a commitment to strengthening co-operation between our two devolved administrations. I therefore welcomed this opportunity to meet my Scottish Ministerial counterpart."
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The Minister continued: "Good transportation routes beyond the sea ports in the South West of Scotland are vital to the North of Ireland.
"I welcomed today, the opportunity to hear of the Scottish Government's plans to upgrade the road network out of these ports and to improve the rail service out of Stranraer. I was also reassured to hear of the long-term priority which the Scottish Government attaches to the transport link across the North Channel."
The Minister added: "I welcomed my Scottish Ministerial counterpart’s commitment to on-going liaison between our two administrations to improve the transport linkages between the North of Ireland and Scotland."
Issues discussed in the meeting included the railway services from Stranraer, trunk road links from the Loch Ryan ports of Stranraer and Cairnryan, the A75 to Carlisle and the A77 to Ayr/Glasgow.
(JM)
