The news agency reported earlier on Saturday that Jordanian security forces had arrested a former adviser to King Abdullah and others on "security related" grounds.
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".
"What has been published about the arrest of Prince Hamzah is not true", said Joint Chiefs of Staff head, Major General Yousef Huneiti.
Abdullah stripped his half-brother Hamzah of his title as crown prince in 2004, saying he had made a decision to "free" him "from the constraints of the position of crown prince in order to give you the freedom to work and undertake any mission or responsibility I entrust you with".
The Petra report said Sharif Hassan bin Zaid, the former royal envoy to Saudi Arabia, and Bassem Ibrahim Awadallah, the former head of the royal court, were detained.
Apart from the members of the royal family, the alleged plot also involved security officials and tribal leaders.
Petra had earlier reported that two senior officials who formerly worked for the palace, along with other suspects, had been arrested for "security reasons", without providing further details.
Hamzah is the eldest son of late King Hussein and his American wife Queen Noor.
He said an investigation was ongoing and its results would be made public "in a transparent and clear form". "King Abdullah is a key partner of the United States, and he has our full support", he said.
Mr Awadallah, also previously served as planning minister and finance minister and has private business interests throughout the Gulf region.
King Abdullah has ruled Jordan since the 1999 death of his father, King Hussein, who ruled the country for close to a half-century. Since then, King Abdullah has been a top US ally, often allowing USA troops to stage operations from Jordanian territory and participating in the anti-Islamic State campaign.
Following the reports, the US Department of State said on Saturday that King Abdullah is a "key partner" of the United States and "has our full support", Reuters reported, citing an email by State Department spokesman Ned Price.
Relations with Israel, meanwhile, are also at a low point, with tensions brewing over Israel's plans to annex the West Bank as well as a series of tit-for-tat diplomatic slights with Israeli Prime Minister Benjamin Netanyahu.
Huneiti affirmed that "no one is above the law and that Jordan's security and stability take precedence over any consideration".
Jordan's economy has been battered by the coronavirus pandemic.
Jordan made peace with Israel in 1994.
Yet he is decidedly less popular at home, where Jordanians often compare him negatively to his father, a deeply popular, charismatic figure who steered the country through many convulsions, including several regional wars, a military coup and more than a dozen assassination attempts. The move was seen at the time as part of Abdullah's consolidation of power five years after the succession.
Abdullah had appointed his half-brother Hamzah crown prince in line with Hussein's dying wish, but in 2004 stripped him of the title and gave it to his own eldest son Hussein.
Jordan's ruling family traces its lineage back to Islam's Prophet Muhammad.
Some of that nostalgia rubbed off on Prince Hamzah, who bears a striking resemblance to King Hussein and was often considered his favorite.