Sinn Féin leader Mary Lou McDonald said she believes that a solution to the political impasse in Stormont can still be reached.
Talks on the restoration of power sharing in Northern Ireland broke down on Wednesday after the leader of the DUP said that there was currently no prospect of a return to devolved government.
Speaking on RTÉ's The Late Late Show tonight, Ms McDonald said: "I would be lying if I said I was anything other than very disappointed that we didn’t manage to get resolution; that it just wasn’t possible for the DUP to get the accommodation that we had arrived at over the line."
"However, I am heartened at the fact that we could arrive at an accommodation. And I think what it demonstrates is that any issue, no matter how vexed, no matter how difficult, does have a solution.
"But the solution can only be delivered with political leadership.
"There is no problem that cannot be solved.
"I don’t buy into the politics of the impossible. I think any problem however big, however complex, if you are sufficiently dedicated and if people are prepared to lead, those problems can be resolved," she said.
"It’s not a good thing that the DUP walked away from the process," she said.
However, she added that "all of this" leads back to sitting around a table. She said that there is no alternative to talks.