Mrs Schiavo, 41, has been without nourishment for almost a week after a judge ordered her feeding tube be removed last Friday at her husband’s request.

Michael Schiavo, who is Mrs Schiavo’s legal guardian, insists she should be allowed to die as that would be her wish.

However her parents, Bob and Mary Schindler, want their daughter to remain alive, saying she is still capable of living a fulfilling life.

While their appeal to the Supreme Court is the latest in a series of legal moves, her parents admit they have few hopes as the Supreme Court has ruled against them on four previous occasions.

“I don’t think that the courts are going to be helpful at all,” Bob Schindler told CNN television shortly before papers were filed.

The appeal to the US’ highest court comes hours after a federal court in Atlanta, Georgia twice rejected appeals calling for the tube to be reinserted.

“Terri is fading quickly ands her parents reasonably fear that her death is imminent,” said family lawyer David Gibbs.

This comes as Florida authorities filed a fresh request for state intervention, amid claims Mrs Schiavo’s condition might have been diagnosed incorrectly.

Florida governor Jeb Bush on Wednesday said a prominent neurologist challenged the notion she is in a vegetative state, saying she is instead in a state of “minimal consciousness”.

But the governor, the brother of US President George W Bush, failed to sway the minds of Florida state legislators who went on to reject a bill that would have forced doctors to reinsert the tube while the case was reviewed.

Mrs Schiavo has been fed artificially for 15 years after heart failure in 1990 left her with severe brain damage.

Her husband has fought her parents and siblings for seven years for her right to die.

Meanwhile 10 protesters including three children have been arrested and handcuffed by police for attempting to get water to her.