The DUP's Sammy Wilson has said he cannot deny there have been "rifts, splits and anger" as a result of the party's change in leadership.
The East Antrim MP told BBC NI's The View it was unfortunate that party divisions had played out publicly.
Earlier the former leader Arlene Foster said she was "sad" at the way she was "taken out of my position".
She said Edwin Poots' ministerial reshuffle didn't show signs of healing, but she was "not entirely surprised".
Mr Wilson told The View: "I don't think any of us are going to pretend that there are not splits and there's not unhappiness, it's played out very publicly unfortunately.
"Those people who have been hurt or unhappy with the way things have been done, there is a real desire in the party to find ways of bringing them back into the fold, of keeping them in the fold if they haven't left, because there's a far, far bigger job to be done."
He added: "You don't go about purging people especially when you've had a leadership election where it's been fairly evenly split.
"Why would you want to purge half the party that didn't vote for the leader.
"That would be just nonsensical, it's not what Edwin's about, it's not what Edwin's supporters are about and it's not what we're about."
Two councillors from County Down have been among a number of party members to quit in recent weeks.
Mrs Foster, who is still Northern Ireland's first minister, said she had loved representing the people of Northern Ireland.
"I am of course feeling a mixture of emotions - sad that I was taken out of my position in the manner that I was taken out," she said following a visit to the Museum of Orange Heritage in Belfast on Thursday.
Mrs Foster will host the British-Irish Council in County Fermanagh on Friday.
Mrs Foster, who is an assembly member for Fermanagh and South Tyrone, said it would be a "nice circle to finish off my local political career" in County Fermanagh.
She said Mr Poots would be there in his capacity as agriculture minister "in my team".
Asked if she would make a final address to the assembly, Mrs Foster replied: "I think that the speaker is going to accommodate me in making a personal statement.
"I haven't spoken to the speaker yet, but hopefully I'll speak to him in the near future."
Mr Poots on Tuesday nominated Lagan Valley assembly member Paul Givan to replace Mrs Foster as first minister.
The move is contingent upon Sinn Féin support.
Once Mrs Foster resigns, Deputy First Minister Michelle O'Neill also steps down as it is a joint office.
There is then a seven-day period allowed for the approval of a new first minister and deputy first minister by power-sharing partners Sinn Féin and the DUP.
Asked if the British-Irish Council would be her last event as first minister, Mrs Foster said she "might" do something on Saturday and Sunday.
Mrs Foster said she hopes all of the New Decade, New Approach deal commitments can be implemented as it was a "compromise on all sides". The deal restored power-sharing in January 2020.
"I think we should move forward and try to look to reconciliation," Mrs Foster said.
Standing alongside Ms O'Neill, as they hosted their final post executive meeting press conference, Mrs Foster said the executive did not have the opportunity to do the things that ministers wanted to do.
"I do of course wish the new executive well as they take on the challenge ahead of them," Mrs Foster said.
Ms O'Neill paid tribute to Mrs Foster and wished her and her family well.
On a visit to Northern Ireland on Thursday, Cabinet Office Minister Michael Gove paid tribute to Mrs Foster and said he believed that Mr Poots would always put the interests of the people of Northern Ireland first.
He said he had worked with the new DUP leader previously and looked forward to continuing to do so.
Meanwhile, former DUP MP Emma Little-Pengelly has said she will not be seeking any further roles within the party.
Ms Little-Pengelly, who has been working as a special adviser to Mrs Foster since January 2020, was the MP for South Belfast between 2017 and 2019.
"I have decided that it is the right time for me to step back and take some time in pursuit of other interests for the next number of years," she said.
She said she had been "deeply saddened" by what had happened "over the last number of weeks, in particular the nature and manner".
"I fundamentally believe in principles of decency, respect, kindness and respect," she said.
She added there is a "huge piece of work to be done moving forward, to bring this party back together".