The fast-moving developments have shocked Jordanians unused to the sort of palace intrigue that has often plagued neighboring countries.
In his video, Hamzah, 41, accused Jordan's ruling class of corruption and stifling freedom of expression.
State-run news agency Petra says among those arrested for "security reasons" were former close aide to royal family Bassem Awadallah.
They had foiled a plot against his half-brother King Abdullah II, who has struck a defiant tone, insisting he will not obey orders restricting his movement.
FILE: Jordan's King Abdullah II (left) laughs with his brother, then-crown prince Hamzah (right), on April 2, 2001, shortly before the Jordanian monarch embarked on a tour of the United States.
Bessma Momani, a professor of worldwide relations at Ontario's Waterloo University, said the house arrest of Hamzah was "self-defeating" because it is likely to strengthen the prince's popularity.
In a video the BBC said it obtained from his lawyer, Prince Hamzah said several of his friends had been arrested, his security detail removed and his internet and phone lines cut.
Prince Hamzah denied being part of "any conspiracy or nefarious organisation", but said the Hashemite kingdom had "become stymied in corruption, in nepotism, and in misrule" and that nobody was allowed to criticise the authorities.
Some 14 to 16 people were arrested, Mr Safadi said, as well as two other senior officials whose detentions had been previously confirmed.
The official newspaper Al Rai on Sunday warned that Jordan's "security and stability" were a "red line that must not be crossed or even approached", and said an official statement on the events was expected later in the morning.
Safadi did not provide specifics on the alleged plot or say what other countries were purported to have been involved.
"This represents another indicator of the implication of outside groups in suspicious activities that were thwarted to protect Jordan and its stability", he said.
"Praying that truth and justice will prevail for all the innocent victims of this wicked slander", she wrote on Twitter.
The pair share a father in the late King Hussein, but have different mothers.
Domestically, Prince Hamzah's unprecedented criticism of the ruling class _ without naming the king _ could lend support to growing complaints about poor governance and human rights abuses in Jordan.
"There is certainly resentment on his part, because he has never digested losing his title of crown prince".
"The army chief of staff came to me and issued threats in the name of heads of security agencies", Hamzah said in the recording.
The Washington Post had first reported that the former crown prince was "placed under restriction" as part of a probe into an alleged plot to unseat the king.
The alleged plot "included at least one other Jordanian royal as well as tribal leaders and members of the country's security establishment", the United States daily added.
Several suspects have been arrested in a security sweep in Jordan, as the army cautioned a half-brother of King Abdullah II against damaging the country's security.
Saudi Arabia, the United Arab Emirates, Qatar, Egypt and other Arab states joined the U.S.in expressing support for King Abdullah.
Reports in November that Israeli Prime Minister Benjamin Netanyahu held secret talks with Saudi Crown Prince Mohammed bin Salman fuelled speculation that a normalisation accord with the Gulf's top power could be in the making.
Israel's Defence Minister Benny Gantz said "Jordan is a neighbour and strategic ally with whom we have peaceful relations".
"We support the steps taken by King Abdullah to maintain Jordanian national security, stressing that Jordan's security and stability is a supreme Palestinian interest".
Awadallah, a US-educated former finance and planning minister, was close to the king but has also been a controversial figure in Jordan.
Before becoming royal court chief in 2007, he was head of the king's cabinet in 2006.
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