Oct 7 (Reuters) - Major stock markets in the Gulf were mixed in early trade on Tuesday as the prolonged U.S. government shutdown tempered sentiment, despite support from higher oil prices.

The White House on Monday backed off President Donald Trump's assertion that government employees were already being laid off due to the shutdown, but warned job losses could result as the standoff looked set to stretch into a seventh day.

Saudi Arabia's benchmark index .TASI dropped 0.5%, on course to snap two sessions of gains, hit by a 1.4% fall in the country's biggest lender by assets Saudi National Bank 1180.SE and a 0.4% decrease in Al Rajhi Bank 1120.SE.

As the U.S. government shutdown extends into its second week, investors are turning to private and alternative economic data to gauge the interest rate trajectory, with a 25 basis point rate cut at this month's policy meeting appearing nearly fully priced in.

The Fed's stance carries heavy clout in the Gulf, where most currencies are pegged to the U.S. dollar, anchoring regional monetary policy.

Dubai's main share index .DFMGI gained 0.6%, with Emirates Central Cooling Systems Corp EMPOWER.DU advancing 2.5%.

In Abu Dhabi, the index .FTFADGI was up 0.3%.

Oil prices - a catalyst for the Gulf's financial markets - extended gains on Tuesday as a smaller-than-expected November output hike by OPEC+ helped to ease some fears of a growing supply glut.

The Qatari index .QSI eased 0.1%, weighed down by a 0.6% fall in petrochemical maker Industries Qatar IQCD.QA.

(Reporting by Ateeq Shariff in Bengaluru; Editing by Mrigank Dhaniwala)

((AteeqUr.Shariff@thomsonreuters.com; +918061822788;))