Sinn Féin leader Mary Lou McDonald has said that she approaches the new round of talks on the restoration of power-sharing in Northern Ireland with "both optimism and pragmatism".
Speaking in Dublin, Ms McDonald welcomed the announcement of the talks.
"This now is our opportunity to resolve the equality issues, the outstanding issues, and to establish good sustainable power-sharing government in the north," she said.
However, Ms McDonald added she believes both the Irish and British governments should step in if agreement cannot be reached.
"If it is not possible to deal with these [outstanding] issues through the talks, well then they will have to be resolved by the two governments, through the inter-governmental conference."
It comes after the Irish and British governments announced the talks, which are due to get under way on 7 May.
In a statement, both governments called for "new thinking" for the talks.
DUP leader Arlene Foster also welcomed the announcement of the talks, and said that the party stands ready to set up the Assembly "without pre-conditions alongside a parallel talks process".
"The DUP will not be found wanting in any talks process but our preference would be for the Assembly to be restored and have the talks process in parallel.
"Talks should respect the three stranded approach and be focused on delivering a fair and balanced deal that both unionists and nationalists can support. Anyone who thinks agreement can be reached through a one-sided wish-list being implemented is not routed in reality," she said.
Northern Ireland Secretary of State Karen Bradley said in a press conference with Tánaiste Simon Coveney in Belfast that it was her "absolute determination" for the new talks to succeed, and that the Good Friday Agreement must be "upheld and defended".
Mr Coveney said he believes all of the parties will approach the talks with a willingness to explore compromise solutions to the problems that have prevented the assembly from getting back up and running for the last two years.
Speaking on RTÉ's Six One News, he said that people in Northern Ireland are demanding a response from politics, particularly following the murder of journalist Lyra McKee last week.
Meanwhile the leader of the SDLP has also welcomed the new talks, however he said that there are concerns that the talks have no "fixed deadline".
In a statement, Colum Eastwood said: "We have concerns, however, that this process with no fixed deadline will simply sink back to the retrenchment of previous talks.
"We have already seen the DUP and Sinn Féin slip back into comfortable red lines that look great on placards but deliver nothing for people desperately in need. Both of those parties need to think again about their approach that's more about seeking a pound of flesh than reaching agreement."
Ulster Unionist Party leader Robin Swann said any talks must be meaningful.
"The Ulster Unionist Party is ready and willing to talk," he said.
"There may be an opportunity for progress, but that will only happen if there is genuine engagement from the two largest parties. The UK government cannot continue to appease the politics of intransigence. They cannot continue to allow Sinn Féin to set the terms for talks."
Additional reporting PA