DUBAI, Jan 24 (Reuters) - Gulf stock markets may consolidate on Tuesday amid a lack of fresh, positive factors, though Saudi Arabia could continue a rebound that began on Monday.

The Saudi index rose 1.7 percent on Monday in the highest trading volume since Jan. 2, closing only marginally below its intra-day high.

Stocks in companies which posted disappointing fourth-quarter earnings rebounded strongly, suggesting investors are looking towards improvement in the non-oil economy this year as the government's introduction of austerity measures slows.

Mouwasat Medical Services could attract interest after saying its board was recommending a cash dividend of 2.5 riyals per share for 2016, up from 2 riyals in the previous year. The company reported an estimate-beating 34.2 percent rise in fourth-quarter profit last week.

The global market environment is marginally positive, with MSCI's broadest index of Asia-Pacific shares outside Japan up 0.4 percent and Brent crude oil slightly above $55.0 a barrel, in its range of the past six weeks.

Kuwait's index, which is up more than 16 percent since the end of last year, rose 0.6 percent in very heavy trade on Monday but showed some signs of losing steam; eight of the 10 most active stocks fell and none rose.

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