Where the main parties stand
DUP
The DUP says the Belfast Agreement is effectively dead and a new deal must be renegotiated.
Buoyant after winning more seats than its Ulster Unionist rivals, it is refusing to share power with Sinn Féin until the IRA officially stands down.
In its election manifesto, the DUP set out seven tests for the outcome of negotiations leading to a new agreement.
These include an insistence that the outcome must provide a settlement within the UK, not a process to a united Ireland; any relationship with the Republic must be fully accountable to the Assembly; only those committed to exclusively peaceful and democratic means should exercise any cabinet-style ministerial responsibility; it must provide stable government for the people of Northern Ireland and not be susceptible to recurring suspension.
The Taoiseach said yesterday some of these issues, such as accountability, stability, efficiency and effectiveness, should be looked at.
While Government officials had placed some hope in pragmatists such as Mr Peter Robinson and Mr Nigel Dodds deviating from party leader Rev Ian Paisley's insistence that there be no negotiation with Sinn Féin, there is no sign that the party will soften its position.
Sinn Féin
Sinn Féin president Mr Gerry Adams says all aspects of the Belfast Agreement must be honoured and has rejected any attempt to renegotiate the deal.
He called yesterday on the British government to lift the suspension of the Assembly and work to ensure all elements of the agreement are implemented.
Mr Adams said: "We want to see the suspension of the institutions lifted but all of the other institutions that are part of the Joint Declaration that we negotiated, the unfinished business of the Good Friday Agreement, we want acts of completion on all of those."
In its election manifesto, the party - which took 24 seats in the Assembly elections - said it would not be deflected from securing the full implementation of the agreement.
"The focus of republicans over the past five years has been to see the Good Friday Agreement implemented ... Our priority now is to see the agreement bedded down, implemented fully, and the peace process stabilised. Sinn Féin will continue to actively develop and advance the potential of the all-Ireland institutions and implementation bodies."
UUP
The Ulster Unionist leader Mr David Trimble has re-stated his commitment to implementing the Belfast Agreement, although he has conceded that some changes may be needed to strengthen the Assembly and Executive.
While there is internal opposition led by the dissident MP Mr Jeffrey Donaldson, who is calling for a complete renegotiation of the agreement, Mr Trimble says there is still a majority in favour of the deal.
The UUP leader has said the Assembly should only be restored when republicans have dealt conclusively with "the issues of decommissioning, continued paramilitary activity and the effective winding-up of their private army".
In its election manifesto, the party gave a long list of achievements secured under the Belfast Agreement, but pointed to the need for reform of the Assembly and Executive.
These issues are likely to be dealt with in the review of the agreement which take place over the coming weeks.
SDLP
The SDLP has pledged to resist any attempts to renegotiate the Belfast Agreement.
Its election manifesto states: "The SDLP will not allow the DUP or anybody else to turn the clock back on progress. We will insist on the agreement's full implementation and development.
"In any review, it will not be the SDLP under pressure - it will be the parties who are falling short of the agreement."
SDLP leader Mr Mark Durkan whose party lost six seats in Wednesday's poll results, yesterday called for the Assembly to be recalled as soon as possible.
"They must not let the DUP hold back progress or turn the clock back on change. Parties who have an increased mandate must show responsibility to break the deadlock," he said.
He also said the agreement's principles, such as partnership government, North/South co-operation, equality and human rights could not be sacrificed.
Compiled by Carl O'Brien