Martin stressed the need for a political resolution that would ensure powersharing returns to Northern Ireland, reports dpa news agency.
The pro-British Democratic Unionist Party (DUP) is currently blocking the formation of a devolved executive at Stormont in protest at the protocol, a set of post-Brexit trading arrangements that have created red tape on the movement of goods across the Irish Sea.
Relations between London, Dublin and Brussels remain strained over the protocol deal that Britain and the EU agreed in 2019 as a way to avoid a hard border on the island of Ireland.
The British government is putting legislation through Parliament that would empower ministers to unilaterally scrap the checks on Irish Sea trade the protocol has created.
It is a move that the EU claims would breach international law.
Martin pledged to work with the incoming Prime Minister, be it Liz Truss or Rishi Sunak, with the aim of securing a return to powersharing in Northern Ireland.
On a visit on Tuesday, Martin was asked how he would engage with outgoing UK Prime Minister Boris Johnson’s successor.
“I think relationships are very important and I’ve always in my political life worked to build relationships with people,” he said.
“And the Irish-British relationship is particularly important.”
He said the UK-Ireland relationship was a “key plank” of the 1998 Good Friday peace agreement.
“So we will work with the new British Prime Minister and we will meet early and engage to work on the very strong issues between us, both bilaterally in the context of economics and so forth and, undoubtedly, in the context of the Good Friday Agreement and the need to have a restoration of the (Northern Ireland) Assembly and Executive and also a strong British-Irish relationship.”