The leaders underscored the importance of preserving the “hard-won gains” of the peace process and the Northern Ireland Executive and Assembly.
In a joint statement, they called for the good faith implementation of international agreements designed to address the unique circumstances on the island of Ireland.
Pressure has been placed on the relationship between Ireland and the UK as the latter voted to leave its membership of the European Union.
The impact of the move on Northern Ireland sparked extended negotiations amid calls to find a method to avoid a hard border being put in place on the island to contend with new differentials in customs and trade arrangements.
However, unionists have voiced opposition to the Northern Ireland Protocol which sees additional checks on goods arriving from Great Britain at ports to avoid a hard land border.
The DUP has urged the UK Government to ditch the protocol.
Mr Biden again stated his support for the Good Friday Agreement in a virtual meeting with Mr Martin on St Patrick’s Day.
“You know my view, and the view of my predecessor of the Obama/Biden administration, on the Good Friday Agreement, we strongly support them, we think it’s critically important they be maintained and the political and economic stability of Northern Ireland is very much in the interest of all of our people,” he said.
Mr Martin responded saying: “It has meant a lot and it has mattered, including as we negotiated Brexit.
“With a new trading relationship now in place between the European Union and the United Kingdom, and a Protocol that protects peace and avoids a hard border on this island, I want to move forward with a positive relationship with the United Kingdom.
“That means standing by what has been agreed and working together to make a success of it.
“That, in turn, can help maintain peace and promote greater reconciliation on our shared island – goals that I know you support.”
Northern Ireland’s deputy First Minister Michelle O’Neill also met Mr Biden on Wednesday.
She praised both the President and Vice President Kamala Harris’s support for the peace process and Good Friday Agreement.
“I thanked them both for their continued political support and emphasised the valued role played by the US administration since the Clinton era,” she said.
“Given the unjust reality where the north no longer has a place in the European Union, our future relationship with Britain itself is now legitimately the focus of widespread public and political discourse as we look to the future of this island.
“I acknowledged and welcomed the Senate Foreign Relations Committee’s bipartisan resolution passed yesterday which expressed full support for the implementation of the Good Friday Agreement, and no hard border in Ireland.
“It also insists that any new US/UK trade agreement must take into account conditions requiring that obligations under the Good Friday Agreement are met.”