The Sinn Fein president, Mr Gerry Adams, believes his party will be the largest in the North by the next election.
At the launch of his party's manifesto for the British general election, Mr Adams predicted that Sinn Fein would win at least three seats, West Tyrone, West Belfast and Mid Ulster.
He said there were also "winnable seats" in Fermanagh-South Tyrone and North Belfast.
Sinn Fein had been "the engine of all the changes that have taken place over the past 10 years" in the peace process and this would continue to be the case in negotiations on the implementation of the Belfast Agreement.
"This time round our vote is going to go up in every single constituency that we are contesting, right across you are going to see a motivated Sinn Fein vote coming out," he said.
His party was also looking forward to the next election in the North, be it for the Assembly or Westminster.
"That is when this party will be not just the largest nationalist party but the largest party in this State," he said.
Mr Adams said he was unconcerned at the prospect of an increase in the anti-agreement DUP vote affecting negotiations.
In its manifesto, the party said it wanted the new Northern Ireland Police Service to be free from "partisan political control, British or unionist", and it should be representative of the community it served, based in the neighbourhoods it served, and be culturally neutral.
Mr Adams said his party would continue to press for Northern MPs and MLAs to be represented in the Oireachtas. The manifesto called for "citizens of the six counties to be given the right to vote in referendums and presidential elections" in the Republic.
The party would continue to demand its right to access to House of Commons facilities, but Mr Adams said it would never take its seats, even if the oath of allegiance to the queen was removed.
He described the issue of non-participation as "a distraction", saying the UUP had a mediocre attendance record, "but those who are at the bottom of the line are the SDLP", with representation "no higher than 5 per cent and as low as 2 per cent".
Sinn Fein's vice-president, Mr Pat Doherty, called for an all-Ireland approach to health, education, environment, economy and the creation of an all-Ireland constitutional court.
He stressed the importance of equality of treatment for the Irish language, heritage and culture. The Minister for Health, Ms Bairbre de Brun, said the party would continue to work for the abolition of the 11-plus selection procedure and fees for third-level education.