Palace officials issued a statement Saturday saying the 81-year-old prince's condition was "worsening," the BBC said.
Rainier has been on a respirator since Tuesday, when his lung infection worsened. Doctors have not yet released a prognosis.
The Pope, who has been absent from Vatican ceremonies for Easter week because of his own ill health, wished Prince Rainier well.
"Informed of the health problems affecting Your Serene Highness, the Holy Father joins with you in thought and prayer with warm wishes towards you," said the message signed by papal secretary of state Cardinal Angelo Sodano.