Taoiseach Micheal Martin will visit Northern Ireland over the coming days, the deputy First Minister has said.
Michelle O'Neill said Mr Martin had spoken on the telephone to her and to First Minister Arlene Foster yesterday.
She believes that the new Taoiseach intends a cross-border visit "at some stage over the next number of days".
Speaking at Stormont, Ms O'Neill congratulated Mr Martin on his election.
"I look forward to working with him in terms of delivering on the commitments of New Decade New Approach and the commitments that were made by both governments," she continued. "I look forward to a good working relationship in the time ahead."
Ms O'Neill said she had raised the issue of the North-South Ministerial Council, which "hasn't met for some time", with Mr Martin. She said one should be held soon.
"I think the North-South Ministerial Council meeting will be an opportunity for us to get to know one another and form good working relationships for the time ahead," she added.
Mrs Foster said she looked forward to meeting the Taoiseach and working with him on "matters of mutual concern for both jurisdictions". She added that she wanted "a positive relationship with him - he is our nearest neighbour and it's important we have a good relationship".
The deputy First Minister expressed her disappointment that no-one from Northern Ireland was among Mr Martin's Seanad nominees.
"It is very unfortunate that they chose not to nominate someone from the North, and particularly someone from the unionist community," she said.
"Ian Marshall's appointment in the past was something that was very positive and very engaging, and something that is right and proper for when we plan for what the future looks like here on this island.
"It is disappointing that one of the first actions that this government has taken has ignored the people of the North."
Mrs Foster said that, as a unionist, she had no view on who the Taoiseach appointed to the Seanad.
"We look to London and the UK in relationship to representation. We don't look to the Republic of Ireland and Dublin," she said.
"It is of course entirely a matter for the Taoiseach as to who he puts onto the Seanad as one of his 11 representatives. It is a matter for him and not really for me."
The deputy First Minister defended her decision to travel to Dublin at the weekend for the formation of the new three-way coalition government of Fianna Fail, Fine Gael and the Green Party.
TDs gathered in Dublin's Convention Centre to officially elect Mr Martin as Taoiseach.
His family didn't travel to Dublin from Cork for the event because of the Covid-19 restrictions in place in the Republic.
Ms O'Neill said she had every right to be there. "Yes, I think it was a good decision to go on Saturday.
"I am the vice-president of an all-island party. It is well within the regulations for me to be allowed to travel to be there and to talk to our strong TD team."
Ms O'Neill added that it was an important day given that "my party president, Mary Lou McDonald was becoming the official leader of the Opposition."
The deputy First Minister's attendance has however been criticised.
Finglas Fianna Fail councillor, Keith Connolly, asked: "On a day when the incoming Taoiseach couldn't have his family in attendance due to Covid restrictions on travel, why did Michelle O'Neill travel to Dublin?"