The monarch held a landmark meeting on Thursday with the Brotherhood's leader Hammam Saeed, secretary-general of its political arm, the Islamic Action Front (IAF), Hamzeh Mansour and other prominent religious figures.
"The Islamic movement has made it clear that the political reforms should start with a modern election law that adopts a system of proportional representation and leads to the formation of a parliamentary government," the statement said.
The Islamic leaders also called for the introduction of "all necessary constitutional and legal amendments that ensure political partnership with all other effective forces in society."
In Jordan the king appoints the prime minister and, to a large extent, Cabinet ministers from people with distinguished records in public life due to the absence of political parties with majority in Parliament.
The Brotherhood seeks to change this state of affairs by turning Jordan into a constitutional monarchy, Islamic sources said.
During Thursday's meeting, King Abdallah acknowledged that the political development process in the country had been thwarted by "hesitation" of officials to carry out the required reforms and by certain pressure groups, which sought to enhance their own interests.
Under pressure from the Jordanian street and opposition parties that drew inspiration from the Tunisian and Egyptian uprisings, King Abdallah sacked the government of Prime Minister Samir Rifai despite its winning a confidence vote with an unprecedented large majority in the lower house of Parliament.
The king's appointment of ex-Premier Marouf Bakhit as new prime minister sparked concerns with Islamists who accused him of "rigging" the 2007 parliamentary elections with the avowed aim of undermining their chances in the election. The IAF then returned only six deputies, compared with 17 in the previous 110-member chamber.
Against this backdrop, the IAF boycotted the Nov. 9, 2010 elections, citing the failure of Rifai's government to come up with an election law that ensures proportional representation in Parliament.
Over 1,000 Jordanians staged a protest against Bakhit in Amman on Friday, calling for his ouster. Islamist and leftist activists protested near the prime minister's office and in downtown Amman. They chanted, "Down with the government".
