Dubai heavyweight Emaar Properties lost 2.5%, while Amlak Finance slid 3.1% and Amanat Holding dropped 3.9%
Gulf stock markets fell in early trade on Sunday after militant attacks in Kuwait and Tunisia killed a total of 66 people last week, and because of concern about the Greek debt crisis.
The main Dubai stock Index sank 1.8 percent. Heavyweight Emaar Properties lost 2.5 percent and two stocks which dominated activity last week fell sharply: Amlak Finance slid 3.1 percent and Amanat Holding dropped 3.9 percent.
Abu Dhabi's market fell 0.5 percent as First Gulf Bank lost 1.3 percent. Qatar dropped 0.4 percent in a broad-based decline.
The Kuwaiti and Saudi Arabian markets were to open later in the morning.
The mosque attack in Kuwait is unlikely to have any significant impact on the country's economy as long as oil exports continue, but the security breach may at least temporarily dampen sentiment among the retail investors dominating that market.
The decision of European Union governments to refuse funding to Athens appears to make a Greek debt default likely and increase the chances of Greece leaving the euro zone.
Global markets have been preparing for a Greek exit for years and could probably now cope with one, and Gulf markets are fairly well insulated from global contagion by heavy government spending. But global equity and oil prices might fall, and this would affect Middle East bourses.