"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.
In the video, he blamed the country's leaders of being 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".
The pair were detained for "security reasons", Petra said, quoting a security source.
Earlier the Jordanian military said it had asked Prince Hamzah not to engage in activities that could be used to undermine the country's security. He also attended Harvard University in the USA and has served in the Jordanian armed forces.
The United States, which considers Jordan a critical ally and has partnered with the country for years on USA -led counterterrorism operations, said that Abdullah had its "full support".
Jordan's neighbours and allies expressed solidarity with King Abdullah over the security measures in the kingdom, an important ally of the United States.
Stability in Jordan and the status of the king has always been a matter of concern, particularly during the Trump administration, which gave unprecedented support to Israel and sought to isolate the Palestinians, including by slashing funding for Palestinian refugees.
In the phone call, King Mohammed VI enquired about the situation in Jordan following reports of an attempted coup d'Etat, a statement from Morocco's royal cabinet has said.
"No one is above the law and Jordan's security and stability are above all", he told the official Petra news agency. "All the solidarity with the Jordanian leadership and King Abdullah in defending the gains of the Jordanian people, protecting their stability, and refusing interference in their affairs".
The swift show of support underscored Jordan's strategic importance as an island of relative stability in the turbulent region.
Security forces in Jordan are understood to have detained almost 20 people in total, including a former adviser to the head of state, on "security related grounds".
The US State Department said on Saturday that King Abdullah is a "key partner" of the US.
"We support the decisions taken by King Abdullah II to preserve Jordan's security and ensure its stability and unity".
Mr Awadallah, an economist who was educated in the USA, has been a confidant of the king and an influential force in Jordan's economic reforms.
The Gulf Cooperation Council, a political and economic union of Arab states bordering the Gulf, has also expressed its support, as did Lebanese Prime Minister-designate Saad al-Hariri and Palestinian Authority President Mahmoud Abbas.
"Ahmed Aboul Gheit added that King Abdullah II has a high and appreciated position, whether among the Jordanian people or on the Arab level in general, and that everyone knows his sincerity and his great role in serving Arab causes".
Noor Al Hussein was the fourth and last wife of King Hussein who ruled Jordan from 1952 until his death in 1999. He has good relations officially with Abdullah, his half-brother, and is a popular figure close to tribal leaders.
While there have been no public quarrels, relations between Hazmah and his half brother King Abdullah II are thought to have been strained since the former was stripped of his title as Crown Prince in 2004.
Awadallah, a former finance and planning minister educated in the United States, was close to the king but has also been a controversial figure in Jordan.
Taiwan prosecutors seek arrest in deadly train crash
However, a third could not be moved before the tracks are repaired while the other five cars were still wedged into the tunnel. The National Fire Service said the dead included the train's young, newly married driver and the assistant driver.
Jordan arrests ex-palace aide, others for ‘security’ reasons
Arrests by senior officials and members of the royal family are rare in Jordan , considered one of the most stable Arab countries. Two people familiar with the situation told Reuters security forces had arrived at his small palace and begun an investigation.