Demonstrators, who accused authorities of being overzealous, threatened to stage a "mother of all demonstrations" next month in the city to close businesses and halt an international sporting event if their demands were not met, the Daily Nation reported Monday.
"Muslims have unanimously agreed that should the government fail to release all Kenyans suspected of terrorism and bring home Kenyans deported to Somalia, we will hold demonstrations to disrupt the (International Amateur Athletics Federation) cross country championships," Sheikh Mohamed Dor said at a rally.
Dor is the head of the Council of Imams and Preachers of Kenya.
The council's treasurer, Sheikh Hassan Omar, added the demand that the head of the special police unit, Commissioner Hussein Ali, be removed from his post.
"Although Mr. Ali is a fellow Muslim, we are very angry with the way he handles cases of suspected terrorists," he said. "It appears that Muslims are being targeted. We therefore demand that he is sacked."
Kenya strengthened security measures along its land border with neighboring Somalia and along its Indian Ocean coast as a result of fighting in Somalia between Transitional Government forces and the Islamic Courts Union, a coalition of Islamist groups, some of which are believed to be linked to al-Qaida.
More than 40 Somali refugees were deported last month because of suspected connections to the ICU, and a number of Kenyans detained over suspected terrorist links.
Mombasa is Kenya's major coastal city, with prime resort areas just north and south of it. The coastal region is predominantly Muslim.