Wakefield's Labour group wants to "move on" from the unrest and internal divisions that have rocked the party for more than a week, according to its chief whip.
Coun Richard Forster said that the majority of councillors wanted to put recent events behind them, after four elected members resigned from senior positions.
It follows an unsuccessful motion to unseat long-serving council leader Peter Box at a Labour group meeting on September 17, amid concerns about Wakefield's failing children's services.
Coun Box said afterwards he intended to carry on in the post he has held for 20 years, but then three Cabinet deputies stepped down.
Coun Steve Tulley also resigned his position on Wakefield's Police and Crime Panel, in protest at the group's leadership, saying it was "time for a change".
But speaking on Wednesday, Coun Forster said that most Labour councillors still support Coun Box.
He said: "Sadly resignations often occur in these situations and I would like to thank the councillors for the work the did whilst in post.
"This does, however, give us an opportunity to bring in new expertise, knowledge and commitment to the Cabinet team and the Police and Crime Panel.
"Recent conversations have shown that the majority of the group want to move on from last week and continue representing the people of the district, delivering the best possible services and giving their support to the leader."
In her resignation letter, Coun Michelle Collins said she was stepping down from her deputy portfolio role for adults and health with "a heavy heart".
She wrote: "I grew up in a foster family and have adopted two children myself, so this is an issue that is very dear to my heart.
"I simply cannot in good conscience allow our children’s services to either fail or be privatised.
"In short, only a change in our leadership can now secure the right future for our council - and far more importantly, the people we represent and serve.
"There comes a time in politics when individuals must be prepared to set aside themselves, take responsibility and act for the greater good."
Coun Jack Hemingway also resigned from his role as Cabinet understudy for communities and environment after last week's full council meeting.
He wrote: "It would not be appropriate for me to continue to serve in the wider cabinet given my support for the children's services/no confidence resolution, and is indeed incumbent on me to resign in such circumstances as a matter of principle."