John Biggs said Tower Hamlets Council looked "very carefully at the appropriate matching" and chose fosterers who could look after the child at a "very traumatic time".
The five year old's case made headlines last week after reports one of the two Islamic households took away her Christian cross necklace and stopped her for eating bacon. Speaking on BBC Radio 4's Today programme, Mr Biggs said these "more sensationalist" claims were "from all of our investigations, not based in fact".
Last week, a judge at East London Family Court decided the child should be temporarily moved to the home of her grandmother, pending further analysis of evidence.
According to Judge Khatun Sapnara, the girl had been placed foster carers in March on an emergency basis after police exercised powers of protection.
She said there had been "no culturally matched foster placement" available at the time.
Since then, the youngster has been placed with two different Muslim families - one for four months and another for two months.
Mr Biggs said: "My understanding is that... the court appoints an independent person who checks into the custody and welfare of the child, and they verified that the child seemed to be in a settled and happy position."
"I wouldn't have a problem with a child being fostered by someone who comes from a different faith but is sensitive to and responds to that child, who communicates with them, who shows their face to that child as well.
The mother of the child said her family had a Christian heritage but the judge said there was evidence to suggest the mother's parents had a Muslim background.
Judge Sapnara said the mother had raised "some concerns" about the "appropriateness" of the placement but had never asked for a change of foster carer.
The judge released an eight-page order last week which described the case as "complex".