The New York Times cited four current and former American officials and Saudis close to the royal family, saying that Mohammed bin Nayef had been "barred from leaving the kingdom and confined to his palace" in the Red Sea city of Jeddah.
A senior Saudi official on Thursday denied a report published by the New York Times that Prince Mohammed bin Nayef was confined to his palace, calling the article "baseless". The report says Nayef was barred from travelling abroad after being replaced by the king's son as next-in-line to the throne.
The official said that Mohammed bin Nayef, a veteran interior minister, was continuing to host guests and there were no restrictions at all on his, or his family's movements.
Mohammed bin Nayef, who was admired in Washington for quashing an Al Qaeda insurgency in the kingdom between 2003 and 2006, was relieved of all his duties a week ago.
In his place as crown prince, King Salman appointed his son Mohammed bin Salman who also serves as defence minister and leads an ambitious reform agenda to end Saudi Arabia's over-reliance on oil.
Mohammed bin Salman's promotion ended two years of speculation about a behind-the-scenes rivalry near the pinnacle of royal power, but analysts said he still has to win over powerful relatives, clerics and tribesmen.
The New York Times, citing four current and former American officials and Saudis close to the royal family, said Mohammed bin Nayef has been "barred from leaving the kingdom and confined to his palace" in the Red Sea city of Jeddah.
Reuters could not reach Mohammed bin Nayef for comment.
But the senior Saudi official expressed shock at the report, which he described as a "fabricated story" and suggested that Mohammed bin Nayef may seek legal action against the newspaper.
"What was published by the New York Times is untrue, completely false, and baseless," the official said, responding to a question on the New York Times report.
"His Royal Highness Prince Mohammed bin Nayef and his family is moving freely and hosting his guests unrestrictedly. Nothing has changed for Prince Mohammed, except for stepping down from his government positions," the official said.
"He hosts guests and leaves his house on a daily basis since he has stepped down. Further, there are no restrictions on his movement whatsoever, either in or outside of Saudi Arabia."
Although Mohammed bin Salman's promotion to crown prince had long been expected among those who follow the royal family closely, the timing was a surprise, and puts the kingdom's future in relatively untested hands.
The promotion proceeded smoothly, with royal family members, senior officials and clerics participating in a traditional ceremony held in the Muslim holy city of Mecca in which they pledged allegiance to the new crown prince.
Saudi state media, eager to show the change was going smoothly, repeatedly broadcast footage of the young Mohammed bin Salman kissing the hand of Mohammed bin Nayef, as his older cousin offered him congratulations.
The Saudi official said Mohammed bin Nayef was "entitled to bring legal action against the newspaper and anyone who defames his reputation by publishing such false news about him."