* BP CEO says oil market is rebalancing

* Lower dollar, new cash inflows help lift crude futures

* Analysts warn that physical oil markets remain weak

By Henning Gloystein and Dmitry Zhdannikov

SINGAPORE/LONDON, April 26 (Reuters) - Crude futures edged up on Tuesday due to a weaker dollar and hopes for an easing of the global oil glut, although gains were capped by concerns that a battle for market share between Saudi Arabia and Iran could intensify further.

Front-month Brent crude futures traded at $44.75 per barrel at 0815 GMT, up 27 cents from their last settlement. U.S. crude futures were also up 27 cents, at $42.91 a barrel.

"Market fundamentals continue to suggest that the combination of robust demand and weak supply growth will move global oil markets closer into balance by the end of the year," BP Chief Executive Bob Dudley said in a statement after the firm reported stronger-than-expected results.

Also helping prices were a weaker dollar and a rush of new investment into crude futures.

However, some analysts warned it was too early to call an end to the crude glut as Saudi Arabia and Iran could ramp up output further in a race for customers.

"The biggest bear risk to the oil market right now is that Iran's ramp-up accelerates and then that Saudi Arabia does the same," Citi said in a note to clients.

"If anyone had a doubt about Saudi Aramco's ability to use its logistical system and spot sales to increase market share, its recent 730,000-barrel sale of a cargo to a Chinese teapot refiner in Shandong should lay any doubts to rest," it added.

The cargo will be lifted in June from Aramco's storage in Japan's Okinawa prefecture and shipped to China's eastern province of Shandong, Reuters reported.

Citi said it was likely that Saudi Arabia was targeting 500,000 barrels per day (bpd) in new sales to bring its production up to at least 11 million bpd.

BMI Research said it had upgraded its Saudi crude production forecast, "reflecting the failure of the meeting at Doha, planned increases in output capacity and the creeping politicization of oil under Deputy Crown Prince Mohammed bin Salman".

On April 17, a deal to freeze oil output by OPEC and non-OPEC producers fell apart after Saudi Arabia, during talks in the Qatari capital of Doha, demanded Iran join in.

BMI said it expected Saudi output to average 10.3 million bpd, up from a previous estimate of 10.2 million bpd.

Iran wants to get back to pre-sanctions production of 4 million bpd.

Traders said a looming gasoline glut in Asia also threatened the recent rise in prices. (Editing by Dale Hudson) ((henning.gloystein@thomsonreuters.com)(+65 6870 3263)(Reuters Messaging:henning.gloystein.thomsonreuters.com@reuters.net))