By Sonali Paul and Trixie Sher Li Yap

(Reuters) -Oil prices edged lower on Friday but were set for a weekly gain with the market continuing to seesaw between fears of a recession hitting the United States and hopes for strong fuel demand recovery in China, the world's top oil importer.

futures fell 13 cents, or 0.15%, to $84.37 a barrel by 0721 GMT, while U.S. West Texas Intermediate (WTI) crude futures weakened 23 cents, or 0.29%, to $77.83 a barrel.

The downturn was partly due to a report on Thursday showing the number of Americans claiming unemployment benefits increased more than expected last week, reigniting recession fears.

"Sentiment overnight seemed to be tilted towards the downside after the jobless data in the U.S.," said Baden Moore, National Australia Bank (OTC:)'s head of commodity research. "However I expect the China demand recovery will be more material to the price outlook into (the second half of) 2023."

An increase in China's consumer price index (CPI) for January compared with December, with inflation approaching the target of about 3% that the government set last year, added an air of caution for the oil market.

"The rise in China's CPI in January reflected the consumption demand of residents before the Chinese New Year, but the data is not as good as expected, reflecting the slow recovery stage of the economy," said Leon Li, analyst at CMC Markets.

"Therefore, oil prices will remain volatile at this stage."

The latest U.S. oil inventory data this week also raised fears about a slowdown in the world's biggest economy, with crude stocks having climbed to their highest since June 2021.

Nevertheless, Brent and WTI have jumped more than 5% so far this week, reversing most of the previous week's losses as concerns about further sharp interest rate hikes by the U.S. Federal Reserve have eased.

The market has been buoyed by Saudi Arabia's move to increase its official crude sales prices to Asia, seen as reflecting a demand recovery in China, where crude runs are expected to increase in March.

"Refiners will likely boost run rates from March to meet domestic demand as well as export needs," said Emma Li, an analyst for China oil markets at Vortexa.

Looking ahead, China's demand will be one of the most important drivers to watch for oil prices, said research director at Wood Mackenzie, Sushant Gupta.

"Indications are emerging of a stabilising or dropping of COVID cases, which will feed into the positive sentiments for oil prices," he said.