The US says an independent Palestinian state should be established through direct negotiations between Israel and the Palestinian Authority and not through UN action
Hawking, 74, who was in Rome to attend a conference at the Pontifical Academy of Sciences and met Pope Francis on Monday, was taken to Rome's Gemelli hospital on Friday.
Both the spokesman and a Vatican source said Hawking, who suffers from motor neurone disease, was not believed to be in serious condition.
The Vatican source said plans for Hawking and his entourage to leave Saturday had not been changed.
Hawking, author of 'A Brief History of Time,' speaks through a computer and travels with a staff of four, including two nurses.
He gave a talk at the Vatican on Nov 25 on the origin of the universe.
The Gemelli is considered one of Rome's best hospitals and it is where popes are treated.