Hamzah, 41, is the son of Hussein and Queen Noor, his American-born fourth wife.
He was declared a crown prince on February 7, 1999, but he was replaced on November 28, 2004 by King Abdullah II's eldest son, Hussein bin Abdullah, who was appointed to the post by his father.
Hamzah is a popular figure in Jordan, widely seen as pious and modest.
In a statement, the Diwan underscored the close fraternal relationship that binds the two Kingdoms, adding that their security is "indivisible".
"The chance to become king escaped him twice: when his father died prematurely - he was too young - and when his brother withdrew his title" of heir, the Jordanian analyst said.
Ibrahim noted that former Prince Hamzah's criticism of corruption and the country's ruling elite "does resonate with some of the king's critics domestically".
He said he told the army chief: "I am not the person responsible for the breakdown in governance, for the corruption and for the incompetence that has been prevalent in our governing structure for the last 15 to 20 years and has been getting worse by the year". "Even to criticize a small aspect of a policy leads to arrest and abuse by security services and it's reached a point where no one is able to speak or express an opinion on anything without being bullied, arrested, harassed and threatened", he added. "As of now, there is no such indication", Oded Eran, a former Israeli ambassador to Jordan and now senior research fellow at Tel Aviv University's Institute for National Security Studies (INSS), told Israel's Army Radio.
"We support the decisions taken by King Abdullah II to preserve Jordan's security and ensure its stability and unity".
The military chief explained that Prince Hamza was asked to "cease any movement and activities that could be used to target the security and stability of Jordan".
The US State Department on Saturday said "We are closely following the reports and in touch with Jordanian officials", Ned Price, a State Department spokesman, said in a statement.
"The king is a red line. we will confront firmly any trembling hand that seeks to tamper with the country's security", former prime minister Faisal al Fayez told parliament in an indirect reference to Hamza.
Jordan, a country of some 10 million people, has been shaken by a series of crises in recent years, from the rise of the Islamic State group in neighboring countries to an influx of Syrian refugees and an economic crisis caused by the coronavirus pandemic. He has cultivated strong ties with several USA administrations, but, in recent years, sparred with former president Donald Trump and Israeli Prime Minister Benjamin Netanyahu over proposed Israeli plans to annex the West Bank and bypass the Palestinians in a bid for Israeli normalization with the rest Arab world.
A former USA 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".
"There is a lot of confusion, but in Jordan, everyone is asking for reform, not to topple the government".
"I recorded this video to make it clear that what has been said officially is not a reflection of what is actually happening on the ground", he said in a video statement. He did not identify the "foreign parties" allegedly involved in the plot.
Dadouch reported from Beirut.