RABAT (AFP) - Thousands of Moroccans demonstrated Sunday in Casablanca, Rabat and other cities calling for more democracy and social justice despite recent promises of deep political reform. About 6,000 people - or 2,000, excluding onlookers, according to the police - marched peacefully through the capital, among them many Islamists and veiled women. An AFP reporter put the number of those marching in Casablanca, some calling for the king's powers to be reduced, at 10,000, while the local authorities put the figure at between 5,000 and 6,000. The protest broke up peacefully. Marches and rallies were planned for other Moroccan towns and cities, among them Fez and Tangier and no incidents were reported. In both Rabat and Casablanca police kept a low profile. Morocco had been largly unaffected by the wave of protest sweeping the Arab world but saw its first nationwide protest last month when young Moroccans set up the "February 20 Movement" on Facebook in the aftermath of the upheavals in Tunisia and Egypt. It called for a further mobilisation Sunday, a month after the first protests. The call for demonstrations was backed by the youth wing of the Justice and Charity movement, regarded as Morocco's main Islamist movement, and by several human rights bodies and non-governmental organisations (NGOs), including the Moroccan Association for Human Rights (AMDH). The left-wing Socialist Union of Popular Forces, part of the governing coalition, also took part in the demonstrations. The February 20 Movement called Sunday's protests despite King Mohammed VI's announcement, hailed internationally by countries including the United States and France, of sweeping democratic reforms, including the introduction of an elected prime minister and broader personal freedoms. Earlier this month the king announced a series of major measures including a commission to revise the constitution, independence for the justice system, separation of powers, and enhanced powers for the prime minister, apparently presaging a move towards a constitutional monarchy. "We want to keep up the pressure so the reforms come about," Seddick Labrack of the NGO Forum for Justice and Truth said in Rabat. "This proves that Moroccans are determind to see through their demands for democracy, social justice, dignity and a true democratic constitution, not what was announced by the king," said Khadija Ryadi, chair of the AMDH. Demonstrators called for a "constitutuion that is the expression of the people's will" and not one "handed out" from on high.