Alliance and the SDLP were the biggest winners in the General Election.
Naomi Long's party became third largest in Northern Ireland taking one seat with Stephen Farry in North Down.
Ms Long said the result benefited those that "committed themselves to go to Westminster to fight the case for NI". She said the parties working together could deliver the best deal for Northern Ireland.
"Winning an election is one thing, actually delivering results is the real challenge. And unfortunately that is the hurdle Northern Ireland consistently fails."
Talks aimed at restoring the Stormont institutions are set to resume on Monday.
Taoiseach Leo Varadkar said all sides should strive to restore power sharing by the January 13 deadline.
"We'll be giving this everything between now and January to get the Assembly and Executive up and running.
"If at that point there is no power-sharing restored in Northern Ireland, we're then looking into another assembly election in Northern Ireland, and I can't imagine who would really want that."
MEP Long said her party would be well positioned to increase its share of seats in the Assembly should a poll be called in the new year, "but most of us would admit we have seen enough elections in the last six months to last a life time".
"But even setting that aside I believe what is best for Northern Ireland is not a further distraction with another election. But what is best for Northern Ireland is that those of us elected back in 2017 deliver an Assembly, actually deliver it," she told the BBC.
"And if we can do that over the next couple of weeks then we will have really achieved something.
"Not just shifting seats at Westminster but actually shifting politics in Northern Ireland to a more progressive and more productive way forward."
Colum Eastwood triumphed in Foyle and secured two seats. They new Foyle MP humiliated Sinn Fein winning with a 17,000 majority. Claire Hanna also celebrated a big victory taking South Belfast from the DUP.
Mr Eastwood said that the huge vote marked a new day for the SDLP.
“This is absolutely a fantastic day for the SDLP,” he said.
"Our vote is up right across the north. We have done very well.
"But we need to listen to what people are saying. This is not about political parties or individual candidates. This is about fixing the problems and getting back to work, because people are sick of it.
"They are sick of the party politics and of the squabbling. They just want politicians to do what they were elected to do. And we are ready to do that.”
The DUP had a bruising night losing two MPs including Westminster leader Nigel Dodds. It's vote was down just over 5%.
Arlene Foster said it was a "hugely disappointing" evening for her party.
"It was very clear in both North Belfast and South Belfast that nationalism came together and decided they were going to get rid of Emma (Little-Pengelly) and Nigel (Dodds)," she said.
She rejected any suggestion the vote called into question her leadership.
"If you look at the votes you will find the greater number of people in Northern Ireland still want to remain within the UK.
"That to me is a very important point."
While Sinn Fein was celebrating de-throning deputy leader Nigel Dodds in Belfast North, it was not a positive poll for the republican party overall with its vote falling across the board.
Michelle Gildernew was the last Northern Ireland MP to be declared. She took Fermanagh and South Tyrone with just 57 votes after the DUP pulled out to give the UUP's Tom Elliott a clear run.
She said focus had to turn to restoring the Executive.
"We have many issues relating to this constituency not least, relating to the news coming from London. We are likely to see the number of years we have to suffer Tory austerity.
"It now looks like things are going to happen that are out of our control but the people of Ireland are ready to take on a new challenge.
"We have a lot of work here to be done to make politics work and we won't be found wanting in that respect. We will be willing to negotiate."