Rotherham Council says it will be "as open and transparent as possible" over an investigation into why it took children away from a foster couple who are members of UKIP.
Council leader Roger Stone also said its officials would meet government representatives, who would report back to Education Secretary Michael Gove.
An internal report on the case was delivered to councillors on Monday.
The couple have told the Daily Telegraph they want the children back.
Mr Stone said: "As we said on Saturday, membership of UKIP should not bar someone from fostering.
"The council places the highest priority on safeguarding children, and our overriding concern in all decisions about the children in our care, is for their best interests.
"We have been able to establish the facts in this case as far as is possible over the weekend, and I can confirm that the children are safe and in very good care.
"However, this remains a very complex case involving legal advice relating to the decision in question, particular features of the children's background and an external agency responsible for finding and providing the foster carers concerned."
Mr Stone said the education secretary had asked for an inquiry relating to this case over the weekend. The council welcomed this and would give "full co-operation" to the department of education, he said.
He said he had already received the internal report that was ordered on Saturday by Paul Lakin, the council's cabinet member for children, young people and families services, and was now "able to set out the way forward".
He said the council's chief executive had invited government officials to meet him and other council officers in Rotherham "so that this information can be rapidly reported to the secretary of state".
He added: "The investigation will focus on the information, advice and evidence gathered before making this decision, the nature of the decision itself and how it was communicated.
"This is a sensitive child protection case. It involves both vulnerable children and the foster carers, so the information the council is able to release publicly is limited by law.
"At all stages however, we will seek to be as open and transparent as possible as we co-operate with the secretary of state."
The children - who are European migrants - were removed by social workers from the council. The couple, who are in their late 50s and have not been named, said social workers had accused them of belonging to a "racist party".
The BBC understands that the three children are all under 10 and one is a baby.
The couple, who have been approved foster parents for seven years, were eight weeks into the placement when they were approached by social workers about their membership of the party.
The wife has previously told the BBC the couple felt they had been meeting the cultural needs of the three children.
Speaking to the Telegraph, she said: "From a personal and selfish point of view, we would like the children back.
"But we are more concerned with the children's welfare, and we do not want them traumatised any more than they already have been. It is not going to be feasible to take these children back. They are the innocent victims in all this. They deserve better."
She went on to say that the couple feel as though they have been "slandered" and would like a public apology from the council.
"We would also like something in the form of a letter stating that they have got it wrong in this case, and that it will not be on our records that we have had children removed from our care. We just want a clean slate."
The husband added: "It is only by us actually doing this that we could help to change things. I don't think we had any idea how enormous it was going to be because we're small people. We're shocked to see it go like it has, but pleasantly surprised."
Rotherham council said they would not comment on this while the report was being considered.
Mr Gove has previously said the "wrong decision" was made "in the wrong way for the wrong reasons" by the council.
He added that the Department for Education, under his leadership, would "ask the necessary questions" to determine what happened in this case, which he also described as "indefensible".
The council's strategic director of children and young people's services, Joyce Thacker, has previously defended the decision, saying it was influenced by UKIP's immigration policy and that she had to "think of their longer-term needs".
Ms Thacker added she did not think UKIP was a racist party, but said it had "very clear" immigration policies which she could not ignore.
The party's leader, Nigel Farage, said he was "very upset and very angry" about the decision and called for "heads to roll" at the council.
Labour's shadow education secretary Stephen Twigg said: "Being a UKIP member should not be a bar to being a foster or adoptive parent, the key factor is whether those parents are providing a safe and loving environment."
Robert Tapsfield, chief executive of the Fostering Network, said the case had to kept in perspective, adding: "There is no evidence to suggest that foster carers are or should be asked about affiliation to mainstream political parties.
"The wider issue is the fact that, for whatever reason, children are on occasion being moved from foster carers when a concern is raised, but before there is a proper assessment and consideration of what is in the child's best interests and before there is any consultation with the foster carer.
"We will be raising this issue again with the children's minister."