CAIRO, April 3 (Reuters) - Egypt's foreign ministry summoned the charge d'affaires of the United Arab Emirates over the case of 11 Egyptians detained in the Gulf state on suspicion of training Islamists to overthrow governments, it said in a statement on Wednesday.

The detainees were arrested in January in a crackdown on what the UAE called an "Egyptian Muslim Brotherhood cell" in the Gulf state, which has previously voiced strong distrust of the Islamist political movement which took power in Egypt last year.

Assistant Foreign Minister for Consular Affairs Ali el-Ashiry called in UAE diplomat Ahmed al-Menhaly and asked him "to convey to the UAE authorities Egypt's concern with completing the investigation of the Egyptian detainees in the security case swiftly," the statement said.

Ashiry also asked that the authorities allow families of the detainees to visit them.

Egypt's Muslim Brotherhood had said in January that some of its members had been wrongfully arrested.

Relations between Cairo and the UAE soured after veteran Egyptian President Hosni Mubarak - a longtime ally of Gulf Arab rulers - was toppled in 2011.

The UAE has voiced distrust of the Muslim Brotherhood that helped propel Egyptian President Mohamed Mursi to power.

In an interview with Reuters this week the police chief of Dubai, Dhahi Khalfan, reiterated charges that the Egyptian movement was linked to an alleged plot to topple the UAE government. (Reporting by Asma Alsharif; Editing by Paul Taylor and Mike Collett-White)