The Daily Mail and The Mirror report that solicitors acting for Ms Winslet – who last week gave birth to a baby son with third husband Ned Rocknroll - have issued the parents' rights group with a legal warning.
It says that the proposed Fathers4Justice ad – which is a reaction to comments about shared parenting the Oscar winner made during an interview with Vogue magazine - would be 'misleading and damaging'.
In the Vogue interview, published in October and quoted in the Express, the actress defended herself from any suggestion that her two children – Mia, 13, with Jim Threapleton, and Joe, nine, with Sam Mendes - may be victims in her two divorces.
In the magazine, she said: "People go, 'Oh, my God! Those poor children! They must have gone through so much.' Says who?"
She continued: "They've always been with me. They don't go from pillar to post; they're not flown here and there with nannies. That's never happened.
"My kids don't go back and forth; none of this 50/50 time with the mums and dads – my children live with me; that is it. That is it!"
In response to these comments, Fathers4Justice created a poster with a photo of Ms Winslet and the slogan: "Kate, every child deserves their father this Christmas."
But when Ms Winslet's representatives heard about the pending campaign, Fathers4Justice said both they and her ex-husband Sam Mendes contacted the organisation.
In a statement to the newspapers, the group said: "In earlier email correspondence with Winslet's agent Donna Wilson, the group agreed to refrain from publishing the advert until 4pm today after representations from Kate Winslet's ex-husband Sam Mendes.
"Donna Wilson said that Mr Mendes claimed the advert was 'false and damaging'."
In a statement to Fathers4Justice, released by the group, Mr Mendes allegedly said: "It is inappropriate for this organisation to involve my family and I when they know nothing of our personal circumstances.
"Whilst I fully support fathers rights I can happily state this has never been a concern for me or my son."
Fathers4Justice said they agreed to delay the poster in order to allow Winslet to confirm or deny whether the Vogue interview was accurate.
Fathers4Justice told The Mirror: "We are running this advert as part of a campaign to highlight the sensitive issue of four million children waking up on Christmas Day without their father.
"It is clear from what Kate says that she does not support 'shared parenting'."