Edwin Poots has asked Arlene Foster for a clear the air meeting following her acrimonious toppling as DUP leader.
Mr Poots was elected as Mrs Foster’s successor in a contest triggered by her resignation as party leader and the North's First Minister.
She was forced out after an internal heave by colleagues unhappy with her leadership.
In an interview with the PA news agency, Mr Poots said his party needed to “heal” following the upheavals of recent weeks.
“I don’t think there’s a nice way of doing things like this,” he said of the revolt against Mrs Foster.
“And ultimately the party’s in a circumstance where it needs to heal and move on and that’s something which I intend to do and intend to drive forward.
“The focus has to be on the issues of the day. And unfortunately politics is a very rough and tumble business. And it may be something which affects me at some point in the future as well.”
Mr Poots said he had spoken with Mrs Foster as part of their ongoing business at Northern Ireland Executive meetings. But he said he wanted to have a one-to-one encounter with the outgoing Fermanagh and South Tyrone MLA whenever she is “able and ready”.
“Obviously I’ve been in meetings with her and spoke to her in those meetings,” he said.
“What I have offered is a one-to-one meeting and I hope that that will be fulfilled.
“Arlene’s pretty busy at the moment, she’s meeting the royal family today and she has other significant meetings this week.
“Whenever she is able and ready I will welcome the opportunity to speak to her.”
Asked if it would provide an opportunity to “clear the air” between them, Mr Poots said: “Yes absolutely. We have worked with each other for the past 15 years. Her and I entered the Executive in 2007 together as ministers and have worked closely on many, many issues.
“And I would hope that we can actually reflect on all of that as we look to the future.”
Attitudes to LGBT community
Mr Poots insisted the DUP will reach out to a broad range of unionist opinion under his leadership.
He is viewed as a traditionalist within the DUP with a conservative outlook on a variety of social issues.
He has faced criticism in the past for controversial comments about members of the LGBT community.
Ahead of his confirmation as DUP leader, Mr Poots said he would treat members of the LGBT community like he would anyone else, as he expressed a desire to create a Northern Ireland where everyone is “free to be what they wish to be”.
The Lagan Valley MLA insisted he did not want to narrow the DUP’s support base.
“Edwin Poots the individual is someone who’s a caring individual who will work for anyone irrespective of their background who wants to see Northern Ireland in a better place for everyone,” he said.
Mr Poots recalled a republican paramilitary murder bid on his late father Charlie as he expressed determination that the North would not slip back to the dark days of the Troubles.
“I am a child of the Troubles – I recognise the impact the Troubles had on my life growing up. We had the hand of death wanted to be inflicted on our own home. Thankfully, it wasn’t successful.
“But I don’t want future generations to be going through that. I want them growing up in a Northern Ireland where they’re free to be what they wish to be.”
Asked what his message to the LGBT community would be in light of some of his past comments, Mr Poots said: “Edwin Poots is going to work for every single person in Northern Ireland, I don’t care what your background is.
“I want you to have a comfortable home. I want you to have good education. I want you to have good health service. I want you to have the opportunity to be what you wish to be in Northern Ireland.
“I want Northern Ireland to be one of the best places in the world to live.”
With new Ulster Unionist Party leader Doug Beattie having signalled an intent to move his party to the centre ground with a more liberal agenda, Mr Poots was asked whether his election as a known conservative potentially represented a realignment of the unionist political spectrum.
“I want to get the broadest swathe of unionist opinion behind the Democratic Unionist Party,” he replied.
“We are the party which represents most unionists. Therefore, I want my reach to be broad and far. If Doug wants to narrow his down, that’s entirely up to him.”