Casablanca, Morocco (CNN) -- A few thousand people turned out Sunday to protest in Morocco, saying the king's proposed constitutional reforms don't go far enough.
Though many expressed support for their king to stay in power, demonstrators argued that a network of privilege and patronage surrounding him must end, and that he must part with more power than he has proposed.
In calling for the protests on Saturday, a member of the Rabat wing said participants are seeking "a truly democratic constitution and a parliamentary monarchy."
"The plan as proposed by the king yesterday does not respond to our demands for a true separation of powers," the organizer said Saturday.
But a Casablanca-based spokeswoman for the reform movement spoke out Saturday against organizing demonstrations, saying, "All Moroccans are happy with the king's speech."
King Mohammed VI of Morocco declared sweeping reforms that will boost the power of the prime minister and take away some of his own.
The revamped draft constitution will make officials more accountable, the parliament in Rabat more dynamic and will give the government greater powers, the 47-year-old king said in a nationally televised address.
The reform movement has called for the creation of a parliamentary monarchy, an end to the influence of the king's inner circle and for a crackdown on corrupt officials. Spain and Britain are examples of a parliamentary monarchy.
In his 30-minute speech Friday, the sovereign described the draft constitution as "a bedrock of the special Moroccan democratic development model -- a new historical bond between the throne and the people," while describing himself as a "citizen king."
His actions followed a series of unprecedented protests in this North African modern Muslim country, where street protests are normally tolerated by the state, unlike in most other Arab countries.
If the draft is ratified in a referendum set for July 1, its most radical change would be empowering voters to select a prime minister, thereby ending the longstanding practice in which the king has selected his own man for the job. The prime minister has tended to take his lead from the sovereign on key matters of state.
If Moroccans back the draft, then the new prime minister would have new powers in decision-making and in day-to-day management -- relieving the king of a number of duties and aligning the style of management along the lines followed by some European Union countries.
In an example of power sharing, the draft constitution empowers the prime minister to dissolve the House of Representatives, and stresses that the king shall consult him before announcing the dissolution of parliament.
"It specifies the conditions to be observed in each case in order to ensure the separation of powers as well as balance and cooperation between the branches," the king said.
Friday's speech stems from a process that was first announced in March, after widespread civil unrest in the wake of the revolutions in Tunisia and Egypt.
The king instructed a hand-picked committee to consult with political parties, trade unions and civil society groups on constitutional changes with a brief to trim the monarch's political powers and make the judiciary independent. But not all civil society groups were consulted, which sparked a wave of demonstrations across the kingdom from groups who feared they would be left out of the new plan.
This move alone -- to grant real power to an elected prime minister -- could satisfy a number of demands from those members of society who have called for change.
Confirming the full authority of the head of government over cabinet members, the draft constitution gives the prime minister the power to propose and dismiss cabinet members.
But King Mohammed will remain a key power broker in the security, military and religious fields, according to the draft. For example, the king would still serve as "the supreme commander of the armed forces" and would not relinquish the power to appoint ambassadors and diplomats under the new constitution. Furthermore, the king would retain the power to dissolve parliament after consultations with the new constitutional court, half of whose members he would have appointed.
Journalist Martin Jay contributed to this report.