Several hundred also rallied in the city in favour of the reforms.
The protest movement, named for the day of its first protest, was inspired by pro-democracy movements across the Arab world.
It has organised protests across the country and pressured the king into offering a series of reforms that curbed his power and boosted the authority of the prime minister, who would become the "president of the government".
But the February 20 Movement says the reform proposals announced by the king in a nationwide address on Friday do not go far enough.
Their call for mass nationwide protests on Sunday went partly unheeded though, as only hundreds of people turned out in several cities for what was intended to be a large demonstration.
In Tangiers, several hundred protested in support of bolder reforms, according to a local journalist who spoke to AFP by phone.
Several hundred others gathered in Marrakesh to denounce the king's proposals, according to an AFP journalist, who said that police did not intervene to disperse the small, peaceful demonstration.
In Rabat, dozens of those opposed to the king's reform were matched by others demonstrating in support of the monarch's Friday speech.
While most political parties reacted favourably to the king's plan, the February 20 movement was unsatisfied from the outset.
"The decision to keep up the pressure was taken before the royal speech because the indications beforehand did not give much hopes of anything positive," economist Fouad Abdelmoumni, who described himself as a "sympathiser" with the movement, told AFP on Sunday.
"The king continues to hold exorbitant powers and in any event, political reform is a long and perilous process," he added.
The 47-year-old monarch, who took over the Arab world's longest-serving dynasty in 1999, currently holds virtually all power in the Muslim north African country, and he is also its top religious authority as the Commander of the Faithful.
Under the new draft constitution to be put to a referendum on July 1, the king would remain head of state and the military and would still appoint ambassadors and diplomats, while retaining the right to name top officials of unspecified "strategic" administrations.
The prime minister will have the power to dissolve parliament, hitherto the monarch's prerogative.
"Compared to the current constitution, this plan is an important advance," Saad Eddine Othmani, an opposition lawmaker of the Justice and Development Party, told AFP Saturday. "Everything the king promised in his speech of March 9 has been kept."
That speech was the king's first since the uprisings that toppled the autocratic rulers of Tunisia and Egypt and came less than a month after the protests erupted in Morocco for more social justice and limits on royal powers.