By Arathy Somasekhar

HOUSTON (Reuters) -Oil prices settled higher on Friday and notched over 3.5% in weekly gains as positive economic data and signals from Fed policymakers that they could cut interest rates as early as September eased demand concerns, while fears of a widening Middle East conflict continue to raise supply risks.

Brent crude futures settled 50 cents up, or 0.6%, at $79.66 a barrel, while U.S. West Texas Intermediate crude futures rose 65 cents, or 0.9%, to $76.84. both benchmarks.

Brent gained more than 3.5% in the week, while WTI rose more than 4%.

"Crude is in a recovery mode ... as geopolitical tensions still seem to be a positive factor, and on-again off-again recession fears have calmed a bit, at least for now," said Dennis Kissler, senior vice president of trading at BOK Financial.

A trio of Federal Reserve policymakers indicated on Thursday that they were more confident that inflation is cooling enough to cut rates. A bigger-than-expected fall in U.S. jobless claims data also helped to underpin the recovery.

The number of Americans filing new applications for unemployment benefits fell more than expected last week, suggesting that fears the labor market is unraveling were overblown and that the gradual softening in the labor market remains intact.

Also offering support was China's consumer price index, which rose last month at a slightly faster than expected rate, statistics bureau data showed.

"Positive momentum was further reinforced by Chinese inflation numbers that exceeded expectations. In this context, it wouldn't be surprising to see the price per barrel testing the $80 level," said Pierre Veyret, Technical Analyst at ActivTrades.

"The price per barrel has benefited from rising geopolitical tensions in the Middle East, which have fuelled fears of a potential conflict that could disrupt the region's output and reduce the global supply of crude," Veyret added.

Israeli forces stepped up airstrikes across the Gaza Strip on Thursday, killing at least 40 people, Palestinian medics said, in further battles with Hamas-led militants.

The killing last week of senior members of militant groups Hamas and Hezbollah had raised the possibility of retaliatory strikes by Iran against Israel, stoking concerns over oil supply from the world's largest producing region.

Iran-aligned Houthi militants have also continued attacks on international shipping near Yemen in solidarity with Palestinians in the war between Israel and Hamas.

Leaders of the United States, Egypt and Qatar on Thursday called on Israel and Hamas to meet for negotiations on Aug. 15 in order to finalize a Gaza ceasefire and hostage release deal.