Qatar expressed its full solidarity with Jordan and its full support to the decisions and measures issued by King Abdullah to preserve security and stability, and boost the process of progress and prosperity, state news agency QNA said.
Former senior officials close to the ruling monarchy were also among those arrested, according to state news agency Petra.
This comes after news that Jordanian security forces arrested a former adviser to King Abdullah, a member of the royal family and others on "security related" grounds, the Petra state news agency said.
Jordan would investigate whether there was a foreign hand in the plot, said the former USA official.
A growing list of Arab countries have voiced their support for King Abdullah. The monarch replaced him with his eldest son, Hussein, four years into his rule.
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".
Majali's niece, Basma, wrote on Twitter that their family house was raided and Majali was taken to an unknown destination.
"Communication was lost with them more than three hours ago", she tweeted.
"I had a visit from the chief of general staff of the Jordanian armed forces this morning, in which he informed me that I was not allowed to go out, to communicate with people or to meet with them because in the meetings that I had been present in, or on social media relating to visits that I had made, there has been criticism of the government or the king", Hamzah said in a video published by the BBC, where he was speaking in English.
Around 20 individuals have been attested in Jordan for "security reasons".
"All the procedures were conducted within the framework of the law and after being required as a result of vigorous investigations", he said.
He stressed that "no one is above the law and that Jordan's stability and security are above all considerations".
Prior to that, The Washington Post reported, citing a Jordanian palace advisor, that some 20 officials were arrested over allegedly plotting a coup d'etat, ousting King Abdullah II and replacing him with Prince Hamzah in a move that could seriously "threaten the country's stability". "King Abdullah is a key partner of the United States, and he has our full support", US State Department spokesman Ned Price said in an email.
Zaid is a distant cousin of King Abdullah II.
Jordan is also home to more than two million Palestinian refugees, most of whom have Jordanian citizenship. Some of that nostalgia rubbed off on Prince Hamzah, who bears a striking resemblance to King Hussein and was often considered his favorite.
Prince Hamzah is the oldest son of the late King Hussein and his American-born wife Queen Noor, and is King Abdullah's half-brother.
The swift show of support, even as Abdullah placed Prince Hamzah under house arrest, underscored Jordan's strategic importance as an island of relative stability in the turbulent region.
He said Sharif Hassan Bin Zeid and former minister Bassem Awadallah, and others, were arrested as part of it. Some sources say he works as a consultant for Saudi Crown Prince Mohammed bin Salman.