DUBAI, March 28 (Reuters) - Most Gulf stock markets were steady or in positive territory in early trade on Tuesday after Asian bourses rebounded, but trading volumes were generally thin.

Emaar Malls added 1.2 percent, outperforming a flat Dubai index . The company had dropped 2.8 percent in the previous two days on news it was making an $800 million bid to acquire e-commerce operator Souq.com, which could put it in a bidding war with Amazon.com . The U.S. company had agreed in principle to buy Souq.com.

On Tuesday, sources told Reuters that Souq.com would make an announcement later in the day about Amazon.com's bid. One of the sources, declining to be identified ahead of the announcement, said the statement would say Souq.com's shareholders had accepted the Amazon bid.

Abu Dhabi's index edged up 0.1 percent and Qatar was flat, with Qatar National Bank climbing 0.6 percent.

The Saudi Arabian index added 0.2 percent after half an hour. Saudi Automotive , which offers services to motorists, saw unusually heavy trading volume and was the most active stock; it surged 4.7 percent.

Riyad Bank lost 2.4 percent and Saudi Public Transport fell 2.3 percent as the two stocks went ex-dividend.

In Kuwait, Kuwait Insurance Co plunged 9.1 percent as it went ex-dividend and the market index slipped 0.3 percent.

(Reporting by Andrew Torchia; Editing by Keith Weir) ((andrew.torchia@thomsonreuters.com)(+9715 6681 7277)(Reuters Messaging: andrew.torchia.thomsonreuters.com@reuters.net))