A total of 108 seats are being contested in Northern Ireland's polls and full results are expected on Friday.
Ian Paisley, the Unionist leader who was re-elected in Ballymena, said on Thursday: "I trust that before long, we will have a government in this country that is pledged and chained and tied to democracy."
Much at stake
At stake is achieving the central aim of the Good Friday peace accord of 1998: an administration drawn equally from the British Protestant majority and Irish Catholic minority that can govern Northern Ireland together.
A moderate-led coalition collapsed in 2002.
The Democratic Unionists and Sinn Fein won in the last assembly elections in 2003, but Paisley rejected the Good Friday pact and refused to talk to Sinn Fein.
"The people have spoken and they have said 'get on with it' and that's what Ian Paisley has to do"
Sinn Fein leader
He has not said he will talk with Sinn Fein this time but seemed at least open to the idea, sparking accusations of betrayal from some former followers.
"I will not be talking to Sinn Fein until they repudiate their terrorism. Let them foreswear their violence, let them turn a new leaf," Paisley said.
Despite IRA disarmament in 2005, Paisley's rivals say that by leaving the door open to power-sharing he has broken a long-time pledge never to "share power with terrorists".
Paisley said he expected to hold talks with Tony Blair, the British prime minister, next week.
Gerry Adams, Sinn Fein's leader, also obtained a comfortable win in his West Belfast constituency.
"The people have spoken and they have said 'get on with it' and that's what Ian Paisley has to do," he said.
The share of the vote is not expected to change much from British parliamentary elections in 2005 when the DUP scored 34 per cent and Sinn Fein garnered 24 per cent.
But both main parties face dissidents within their own constituencies who accuse them of betraying their principles.
Failure by Northern Ireland's parties to form a government by March 26 will see Britain carrying out its threat to impose indefinite direct rule, with help from Dublin.
Blair and his Irish counterpart Bertie Ahern are due to meet in Brussels on Friday.
Ahern welcomed the good showing by parties seen as ready to accept power sharing.
"I think their position has been vindicated, so that's good."