Prince Hamzah denied being part of "any conspiracy or nefarious organisation", but said the Hashemite kingdom had "become stymied in corruption, in nepotism, and in misrule" and that nobody was allowed to criticise the authorities.
Abdullah has ruled Jordan since the 1999 death of of his father, King Hussein, who ruled the country for close to a half-century.
He said his security has been removed and the internet and phone lines have been cut.
Gen. Yousef Huneiti issued a statement saying Hamzeh had not been detained but instead was "asked to stop movements and activities that were being employed to target Jordan's security and stability", adding that "all the procedures were conducted within the framework of the law and after extensive investigations".
Army chief Yusef Huneity earlier denied reports that Prince Hamza had been arrested.
Arrests of top officials and royal family members are rare in Jordan, a key western ally that has proven a vital partner to the USA particularly in its fight against terror groups in neighbouring Syria.
The U.S. considers Jordan a major ally, granting it access to military equipment and assistance. The kingdom hosts some 3,000 American troops.
Arrests of top officials and royal family members are rare in Jordan, seen as one of the Arab world's most stable countries.
"The Arab Republic of Egypt expresses its full solidarity and support to [.] His Majesty King Abdullah II bin Hussein in maintaining the security and stability of the kingdom against any attempts to overthrow [him]".
He has also served as an adviser to Saudi Crown Prince Mohammad bin Salman.
Israeli Defense Minister Benny Gantz called Jordan a "strategic ally" and dismissed the turmoil as an "internal Jordanian matter".
Stability in Jordan and the status of the king have always been matters of concern throughout the region, particularly during the Trump administration, which gave unprecedented support to Israel and sought to isolate the Palestinians, including by slashing funding for Palestinian refugees.
Jordan made peace with Israel in 1994.
In early 2018, as then-President Donald Trump was threatening to cut aid to countries that did not support US policies, the administration boosted assistance to Jordan by more than $1 billion over five years.
Abdullah and Hamzah have not displayed any open rivalry over the years.
He criticized the Jordanian government, claiming it is responsible for the deteriorating human rights situation in the country.
"There's no question that there's been a real degradation in the space for critical political conversation and in terms of basic freedoms", he said. The king has cultivated close relations with USA and other Western leaders over the years, and Jordan was a key ally in the war against the Islamic State group.
Jordan, which is now under a nightly covid curfew that is set to expire in mid-May, has been hit hard economically by the coronavirus pandemic as well as by the fallout from massive waves of refugees from neighboring Syria. Unemployment has skyrocketed to some 25%, while the country has been saddled with an influx of some 1 million Syrian refugees. He has good relations officially with Abdullah, his half-brother, and is a popular figure close to tribal leaders.
Abdullah stripped his half-brother Hamzah of his title as crown prince in 2004, saying he had chose 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".