UPDATE 6-Oil up about $1 bbl, set for weekly gain on Saudi output cut

* Brent, WTI set for weekly gains of more than 6%

* Rally in global equities also feeds appetite for risk

* Latest global lockdowns delay fuel demand recovery (New throughout, updates prices, market activity and comments; new byline, changes dateline, previous LONDON)

NEW YORK, Jan 8 (Reuters) - Oil prices hit 11-month highs and were on track for a weekly gain on Friday, supported by Saudi Arabia’s pledge to cut output and strong gains in major equity markets.

Brent crude climbed 1.04 cents, or 1.9%, to $55.42 a barrel by 11:33 a.m. EST (1633 GMT), the highest since late February, and U.S. West Texas Intermediate (WTI) gained 82 cents, or 1.6%, to $51.65, also its highest level since late February. Both benchmarks were on track for weekly gains of more than 6%.

“People are realizing the market is tighter than it has been in a while and that the commitment by Saudi Arabia to cut back production is going to keep the market balanced despite the concerns about shut-ins from COVID,” said Phil Flynn, senior analyst at Price Futures Group in Chicago.

Saudi Arabia this week pledged extra, voluntary oil output cuts of 1 million barrels per day (bpd) in February and March as part of a deal under which most OPEC+ producers will hold production steady during new lockdowns.

In a sign of tighter supply following Saudi Arabia’s cut, seven North Sea crude cargoes were bought and sold in the trading window operated by Platts on Thursday. Normally, just one or two cargoes change hands each day.

Analysts said oil prices could see a correction in the coming months if fuel demand remains constrained by the pandemic. Strict restrictions on travel and other activity around the world to contain a surge in COVID-19 cases are weighing on fuel sales, weakening the prospect of an energy demand recovery in the first half of 2021.

The pandemic claimed its highest U.S. death toll yet this week, killing more than 4,000 people in a single day, while China reported the biggest rise in daily cases in more than five months and Japan may extend a state of emergency beyond the greater Tokyo region.

Global shares were rallying, with Japan’s Nikkei hitting a three-decade peak, as investors focused on hopes for an economic recovery later in the year. (Additional reporting by Bozorgmehr Sharafedin in London and Yuka Obayashi in Tokyo; Editing by Elaine Hardcastle, Alexander Smith, Barbara Lewis and David Gregorio)