The Washington Post said Jordanian authorities detained Hamzah and arrested almost 20 other people after what officials called a "threat to the country's stability".
The Petra report said Sharif Hassan bin Zaid, a member of the royal family, and Bassem Ibrahim Awadallah, a former head of the royal court, were detained.
Following "comprehensive investigations by security services", Hamzah was "asked to stop activities and movements that are employed to target the security and stability of Jordan", al-Hunaiti said in a statement. Army chief Yousef Huneiti did not specify what such actions were and denied reports that Hamzah had been arrested.
Hajraf stressed that the security of Jordan is part of the GCC states' security.
Army chief Yusef Huneity earlier denied reports that Prince Hamza had been arrested.
"It's a very sad and unfortunate turn", he added.
Abdullah has ruled Jordan since the 1999 death of of his father, King Hussein, who ruled the country for close to a half-century.
After the arrests, the Saudi royal court expressed full support for King Abdullah, as well as Egypt, Lebanon and Bahrain.
"The move followed the discovery of what palace officials described as a complex and far-reaching plot", it said, quoting a senior Middle East intelligence official.
A former US official with knowledge of the events in Jordan said the threat did not involve a physical coup.
A former United States official familiar with the actions in Jordan said the alleged plan would not involve a "physical coup" but protests that would appear to be a "popular street insurgency".
US Capitol on lockdown due to security threat
The attack took place close to where armed insurrectionists stormed the complex housing the US Congress on January 6. The US Capitol Police said the investigation into today's attack on police officers near the US Capitol is ongoing.
Prince Hamza is not seen as a major threat to Jordan's monarchy and he has been marginalised for years. But the authorities have become increasingly concerned with his efforts to build ties with disgruntled figures within the powerful tribes.
These people known as the Herak have in recent weeks called for protests against corruption in a country hit hard by the impact of Covid-19 on the economy, pushing unemployment to record levels and deepening poverty.
The Washington Post said the alleged plot "included at least one other Jordanian royal as well as tribal leaders and members of the country's security establishment".
"The US administration knows that Bassam Awadullah works for MBS (Mohammed bin Salman)".
In late March, media reported that Jordan had unveiled a new defense agreement with the United States, which allowed free entry of American military personnel, aircraft and vehicles into the Kingdom.
Jordan's former Crown Prince Hamzah bin Hussein has sent a video message through his lawyer, saying he is under house arrest and criticising the way the country is being governed.
Government officials were not immediately available for comment.
Sherif is a title given to those close to the royal family in Jordan.
Jordanian security forces have arrested top officials and others on "security related" grounds, according to Petra news agency.
FILE - In this December 10, 2020 photo released by the Royal Hashemite Court, Jordan's King Abdullah II gives a speech during the inauguration of the 19th Parliament's non-ordinary session, in Amman Jordan.
The tradition of the ruling Hashemite dynasty under the 1952 constitution gives the crown to the eldest son, but the monarch retains the option of naming a brother to be next in line. He said but this was a warning from him, from the chief of police and from the chief of the security services the Mukhabarat, that I should not leave my house, that I could only visit family, that I could not tweet, and that I could not communicate with people.
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