* Oil prices on track for second week of gains
* Optimism on OPEC extending cuts buoys prices
* Russia backs extending production cut (Updates throughout, changes dateline, previous TOKYO)
LONDON, May 19 (Reuters) - Oil prices were heading on Friday for a second week of gains on growing expectations that big crude exporters will extend output cuts to curb a persistent glut in inventories.
Brent crude was up 63 cents at $53.14 at 0813 GMT, after climbing to $53.20, its highest since April 21. U.S. benchmark crude oil was up 61 cents at $49.96 a barrel.
Since the start of March, the Brent price has swung from more than $56 a barrel to less than $47 as opinion has swayed over whether cuts by the Organization of the Petroleum Exporting Countries and other producers will offset rising U.S. output.
"The battle between bulls and bears is raging on oil," said Greg McKenna, chief market strategist at futures brokerage AxiTrader.
"On the one hand, you have traders who worry about the efficacy of OPEC's oil cuts on inventory levels. On the other, there are those who are focused on the real drawdowns that have started to occur in U.S. oil stocks over the past month or so," he said.
Saudi Arabia and non-OPEC Russia have said they want an extension to output reductions of almost 1.8 million barrels per day (bpd) that were initially agreed to run in the first half of 2017.
OPEC and other producers are due to discuss an extension during an OPEC meeting on Thursday.
"I think the cuts are enough to stabilize the market. I think they will likely bring some stock draws but I don't think it will bring the stock draws that OPEC is hoping for," said Olivier Jakob, managing director at Petromatrix.
Russia's largest oil producer Rosneft said on Thursday it was ready to stick to crude output agreements with OPEC.
Still, there are signs that Saudi Arabia, OPEC's largest producer, is keeping markets well supplied. Its crude exports rose by 275,000 bpd in March from February and its stockpiles also increased, official data showed on Thursday.
(Additional reporting by Aaron Sheldrick and Henning Gloystein; Editing by Edmund Blair)