David Cameron has said he has "every sympathy" with the parents of a severely disabled girl who say he has reneged on a pre-election pledge.
Celyn Vincent has severe quadriplegic cerebral palsy and epilepsy and requires round-the-clock care.
Her parents say they may have to put the six-year-old into care as they receive just six hours respite a week.
Celyn's mother Riven has criticised Mr Cameron and said the family was "crumbling".
At a Downing Street press conference the Prime Minister said: "I have every sympathy with the incredible difficulty that families have with bringing up disabled children, particularly when, as in the case of Riven's child, they are quadriplegic and have to have a huge amount of help around the clock, 24 hours a day."
Mr Cameron, whose son Ivan suffered from cerebral palsy and severe epilepsy and died in 2009 aged six.
"I have experience of this myself, and I know how tough and hard it can be, and how so many families can get to the end of their tether and just not know how they are going to go on caring for someone they absolutely love and feel a great joy from, as well as a huge amount of challenge in their lives.
"Obviously, I'm going to look into this case very closely and have already started to do that."
Mr Cameron said he understood South Gloucestershire Council had been in touch with the family since the story emerged to see if more could be done to help keep Celyn - the Welsh equivalent of Holly - at home.
He visited the family at their home in Bristol last April, after which they believed he would do more to help carers if he became prime minister.
But, in a desperate plea posted on the parenting website Mumsnet on Wednesday, Ms Vincent announced that she had asked social services to take Celyn into care.
It provoked hundreds of messages of support.
In a statement on Thursday, the mother criticised Mr Cameron for failing to improve the plight of carers.
She said: "No one government is to blame. But I had hoped that, after David Cameron came to visit me earlier this year following our exchange on Mumsnet, he would have done more to protect families like ours.
"The money the Government has allocated for short breaks and respite care - £800 million over four years - is not enough, and, worse still, it's not going to be ring-fenced. So there's nothing to stop cash-strapped local authorities from using the money elsewhere."
Ms Vincent explained the conditions that led to her desperate cry for help: "Caring for my daughter is relentless. She needs someone 24 hours a day.
"She must be tube-fed, is doubly incontinent, cannot walk, talk, sit up, or use her arms. She has to be lifted using a hoist from chair to wheelchair, between bed and bath.
"She doesn't grow up. I sleep in a bed next to Celyn every night, beside a monitor that checks her breathing. I've barely had an unbroken night since she was born and I am exhausted."
Ms Vincent added that she was so tired through sleeplessness that she was unable to cook or give her three other children the attention they need.