Sinn Féin President Gerry Adams said in Dublin this evening that the mandate given to his party in the Stormont Election was a massive endorsement of their peace strategy.
Mr Adams added that it was a vote for the Good Friday Agreement and political progress.
He said the voters wanted to see the power-sharing institutions up and running by 26 March and there was now a huge responsibility on those elected to make this happen.
Mr Adams was speaking at the launch of Sinn Fein's campaign for the forthcoming General Election south of the border.
DUP, SF win most seats in NI Election
Counting has been completed in the Stormont Assembly elections, with the DUP and Sinn Féin taking the most seats.
The SDLP will be entitled to just one of the ten ministerial positions in the incoming executive.
The DUP will have four positions and Sinn Féin three, leaving three jobs to be divided between the SDLP and the Ulster Unionists.
The positions are shared out on the basis of Assembly seats won and the Ulster Unionists have more seats than the SDLP.
The unionist bloc - four DUP ministers and two from the UUP - compares to Sinn Féin's three and the SDLP one, a total of four.
With all 108 seats declared, the DUP have 36 members elected, and Sinn Féin 28.
The Ulster Unionists have 18 MLAs, and the SDLP has 16 MLAs.
The Alliance Party has seven seats, with Hong Kong born Anna Lo making history by becoming the first person from an ethnic minority background to win a seat.
The loyalist Progressive Unionists are also celebrating a victory for their leader, Dawn Purvis, who held on to the late David Ervine's East Belfast seat.
Brian Wilson in North Down has meanwhile become the Green Party's first candidate to be elected to the Assembly. Independent Dr Kieran Deeny retained his seat in West Tyrone.
US congratulates Northern Ireland
The US Administration has congratulated Northern Ireland on a peaceful and successful election.
Spokesperson Sean McCormick said it was now time for the political leaders to stand up the Stormont Assembly and address the interests of all the people of Northern Ireland.
He said the US shared the commitment of the Irish and British governments in ensuring the full implementation of the St Andrews Agreement.
Taoiseach Bertie Ahern and British Prime Minister Tony were commended for their 'concerted, sustained efforts towards ensuring a lasting peace in Northern Ireland'.
Bertie Ahern and Tony Blair have said the results of the Northern Assembly elections showed a clear message that the people wanted a return to devolved government.
At a news conference in Brussels, where both men are attending the EU summit, they said the campaign had been fought on bread and butter issues, such as water charges.
The Minister for Foreign Affairs, Dermot Ahern, urged the DUP to make what he called a 'giant leap' by accepting to enter government with nationalists.
British Northern Secretary Peter Hain was scheduled to hold meetings with Mr Adams and DUP leader Ian Paisley today.
Speaking on RTÉ Radio's Morning Ireland, Mr Hain said the people have voted for power-sharing.