Christian Leclerc, the conservative mayor of Champlan, about 23 kilometres south of Paris, reportedly explained his refusal on the grounds that the cemetery has "few available plots".
"Priority is given to those who pay their local taxes," Leclerc was quoted as saying by Le Parisien daily today.
However, amid uproar in France over the incident, Leclerc told AFP today his words had been "taken out of context" and he had been a victim of the "wrong interpretation".
Leclerc said he was "really sorry" that the story had become such big news and said he would offer his condolences to the family.
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Before the denial, Laurence Rossignol, a junior government minister for the family, said on Twitter the refusal was "an inhumane humiliation" for the family, adding the hashtag #honte or "shame".
And France's defender of human rights, Jacques Toubon, said he was "shocked, stunned by the news".
The baby, identified only as Maria Francesca, was born on October 14 and died in the early hours of December 26.
Maria Francesca was rushed to hospital in nearby Corbeil-Essonnes, where she was pronounced dead from sudden infant death syndrome.
The family asked a burial firm in Corbeil-Essonnes to request permission from the authorities to lay the infant to rest but, according to the firm's manager Julien Guenzi, the mayor refused "without explanation".
"He doesn't have to justify himself, but responses like that are very rare," Guenzi told AFP.
The mayor of Wissous, a few kilometres away, has since offered to host the burial, telling AFP it was a "a question of humanity".
"The pain of a mother who carried a child for nine months, and lost her after two and a half months must not be worsened," mayor Richard Trinquier told.