Theresa Villiers and Charlie Flanagan both attended a meeting to review the implementation of the Fresh Start deal negotiated in November last year.
Both the British and Irish governments said the momentum created by the agreement must be maintained.
Mrs Foster became Northern Ireland's first female first minister on Monday.
The Democratic Unionist Party leader took over from Peter Robinson, who confirmed his resignation in the Northern Ireland Assembly.
Mrs Foster is the youngest person to hold the most senior post in Northern Ireland politics.
Speaking after Thursday's meeting, Mrs Foster said she was "absolutely delighted" by how the Fresh Start agreement had been implemented.
"Good progress has been made and we'll continue to make that progress," she added.
She said the legacy of Northern Ireland's Troubles had been discussed and that there was a need to talk to victims' groups.
Earlier, Northern Ireland Secretary Theresa Villiers said "significant progress" had been made since the Fresh Start agreement was made, but "substantial challenges" remained.
She added: "Work continues with victims' representatives and others on finding a way forward to address the legacy of Northern Ireland's past."
Arlene Foster has had her first meetings since becoming first minister with the Northern Ireland secretary and the Irish foreign minister.