UPDATE 9-Oil posts best quarter since mid-2015 but glut still worries

(In paragraph 6, corrects Brent June settlement figure to $40.33, not $39.75)

* Brent, U.S (Other OTC: UBGXF - news) . crude up double digits this month, most since April

* Rally could fade as output freeze falls short of expectations

* Brent price seen averaging $40.90, WTI $39.70 in 2016- Rtrs poll

By Barani Krishnan

NEW YORK, March 31 (Reuters) - Oil prices jumped more than 10 percent in March in the best quarter since mid-2015 although some analysts said the rally could fade soon as an output freeze plan by major crude exporters fails to alleviate worries of a glut.

A weak dollar and data showing a drawdown in crude stocks at the U.S. futures delivery hub helped oil settle steady to firmer in Thursday's session.

But traders remained worried that a tentative agreement among the world's largest producers to keep oil output at January's levels will barely make a dent on global supplies.

Analysts said crude futures also appear to have overextended gains with a 50 percent rally since the deal was proposed mid-February, amid little improvement in fundamentals.

"Oversupply still persists due to resilient U.S. production, even if declining moderately; high OPEC output, led by Saudi Arabia and Iraq; and the gradual return of Iran starting Q1 2016," said Mike Wittner, global head of oil research at Societe Generale.

Brent crude for May delivery, which expired as the front-month contract, settled up 34 cents, or 0.8 percent, at $39.60 a barrel. June Brent closed 0.7 percent higher at $40.33.

The benchmark's front-month soared 10 percent higher in March - its best month since April 2015 - and jumped 6 percent in the first quarter - its best quarter since the second quarter in 2015.

U.S. crude futures settled at $38.34, up 2 cents on the day, rising 14 percent in March and 4 percent in the quarter - also its biggest quarterly gain since June 2015.

In a Reuters poll, oil analysts raised their average price forecasts for 2016 for the first time in 10 months - Brent averaging $40.90 and U.S. crude $39.70 in 2016 - but cautioned the rally could fade near term.

On Thursday, the dollar hit a mid-October low, making greenback-denominated oil more attractive to holders of the euro and other currencies.

Data from market intelligence firm Genscape showed a 807,496-barrel drawdown in stocks at the Cushing, Oklahoma delivery hub for U.S. crude futures in the week to March 29, traders said.

Inventories at Cushing have receded from record highs for two consecutive weeks, with U.S. government data on Wednesday showing a 272,000-barrel drawdown in the week ending March 25.

Total U.S. crude stocks, however, rose 2.3 million barrels last week to 534.8 million barrels, a record high for a seventh straight week.

OPEC crude output rose in March to 32.47 million barrels per day from 32.37 million bpd in February, a Reuters survey said.

Analysts also expect an April 17 meeting of major oil producers in Doha to discuss the output freeze to fall short of expectations.

"There is a clear risk of disappointment and for a temporary setback in prices ahead or immediately after the Doha meeting," Carsten Fritsch, commodities analyst at Commerzbank (Xetra: CBK100 - news) , told the Reuters Global Oil Forum.

(Additional reporting by Libby George in LONDON; Editing by Marguerita Choy)