The DUP leader made the comments on Wednesday.
Northern Ireland goes to the polls on 2 March after the political fall out over the Renewable Heat Incentive scandal led to a snap election.
"We need now to get to the far side of the election so that we can put these institutions back in place to make them work," she said.
Mrs Foster added she would lead the party into the election "front and centre."
"My political opponents and certain sections of the media have characterised me in a certain way," she said.
"I believe the people of Northern Ireland know exactly who I am.
"I'll be going out and around Northern Ireland, they can speak to me, they can talk to me.
"Everyone knows I'm very open to people coming and having those conversations.
"We now have an election that has been caused by one of the partners in government walking away.
"We need to look at that because it has brought us instability instead of working through the difficulties that have presented themselves.
"All I know is I'm still the same person who stood for election in May of last year, I still have the same priorities, I still want to implement my five-point plan for Northern Ireland and that's what I will be asking the people of Northern Ireland to let me do."
Later on Wednesday, Prime Minister Theresa May spoke with Mrs O'Neill and said she looked forward to working with her.
Mrs May said she hoped that following the election "all parties would be able to come together to find a way forward for Northern Ireland".
Mrs O'Neill said she used the occasion to raise a series of matters including legacy issues and the Fresh Start Agreement.
She said she told the Prime Minister that equality and respect must be at the heart of any new power-sharing executive.
Arlene Foster has said she will "have to work with" the new Sinn Féin leader north of the border, Michelle O'Neill.