The MRC denies accusations of violence and said the four people arrested on Monday were had no links to the group.
The Portuguese built it in 1591 to watch over the port of Mombasa, then one of the richest city states in the east coast of Africaç
Ten more people were also wounded in the shootout, Kenya's Mombasa County authorities said.
The ship, named the MV Al-Noor, had been intercepted by the Kenya Navy two weeks ago off the Lamu coast, some 350km north of Mombasa.
Authorities urged the Muslim community to remain calm after Sheikh Mohammed Idris was killed on Tuesday.
The new arrests – which targeted Mombasa's Majengo and Town center – take to 490 the number of suspects detained in Mombasa since Sunday.
Mombasa has recently been the target of several deadly bombings.
A man left a bag outside the doors of the Summerlink Hotel and disappeared, prompting somebody to raise an alarm.
Four people were killed in the Saturday night blasts.
Sheikh Abubakar Shariff, a scholar popularly known as Makaburi, was gunned down on Tuesday by unknown attackers in the Shanzu area in Mombasa.
Kenya opposition members of parliament to take legal action against government over storming of Masjid Musa Mosque.
Kenyan police stormed the Masjid Mussa mosque in the city's run-down Majengo neighbourhood on Sunday.