On the eve of a conference to fine-tune Kenya's new constitution, several thousand Muslims demonstrated peacefully to demand that religious courts be retained.
Christian groups object to mention of Muslim courts in the constitution, which does not mention other religions.
A monthlong National Constitutional Conference opened this week in Nairobi, the Kenyan capital.
Provision for so-called khadi courts was included in Kenya's current constitution, drafted before independence from Britain in 1963, in line with a treaty among Britain, Kenya and the Sultan of Zanzibar.
The sultan relinquished his claim to a 10-mile-wide strip along Kenya's seacoast in return for guarantees to Muslim residents there that included religious courts to handle personal matters.
A government-appointed chief khadi in Mombasa is the senior authority for Kenya's Muslims.
Mohamed Dor, secretary of the Council of Imams and Preachers of Kenya, told the Mombasa demonstrators "the khadi court must be enshrined in the new constitution or else we will secede."
Some Muslim leaders say Kenya's Muslims are a third of the population; academics put the number closer to 5 percent.