The Taoiseach has expressed confidence that there will be a strong pro-agreement majority in the new Assembly.
Mr Ahern plans to hold talks with representatives of the parties supporting the Belfast Agreement, starting next week.
Reacting cautiously to the continuing Northern counts, he said it looked as if nationalists and republicans were performing strongly and the Alliance Party was also doing well. It looked as if Mr David Trimble was not doing as well as he might have expected, said Mr Ahern, but he was hopeful they would see pro-agreement candidates transferring to each other.
Mr Ahern said he looked forward to working with whoever won and to implementing the Belfast Agreement. He would like to see the Ulster Unionist Party getting a good share of the vote. "But, ultimately, I want to see those people who are in favour of the agreement working together," he added.
The Fine Gael leader, Mr John Bruton, said the large vote across the electorate for candidates supporting the full implementation of the agreement showed a commitment to peace, regardless of party background.
The newly-elected representatives had to make coalition-building a success, he said. The problems in Northern Ireland could now be approached with the support of a large majority of the people. The negotiations to make the new institutions work would be no more difficult than making the agreement in May.
Welcoming the results, the leader of the Labour Party, Mr Ruairi Quinn, said the people of Northern Ireland had given overwhelming backing to candidates and parties who supported the agreement. He was particularly pleased with the excellent performance of Labour's sister party, the SDLP.
The establishment of the Assembly and the structures of government that would emerge over coming months marked a historic departure in the politics of the island, Mr Quinn added.
The Democratic Left leader, Mr Proinsias De Rossa, said the most significant factor to emerge from early returns was the strong support for pro-agreement parties and candidates.
Urging everyone to resist any temptation to try to exploit Mr Trimble's situation for short-term party advantage, he said that he was entitled to great credit for the honourable and courageous role he had played in negotiating and promoting the agreement "and remains a crucial figure, leading a new, progressive unionism".
Meanwhile in New York, the President, Mrs McAleese, said that whatever the final outcome of the election, the members of the new Assembly had "a sacred duty to start the process of consensus".
