* Saudi Arabia hikes June crude oil prices for most regions

* US oil rig count falls by 7 to 499, Baker Hughes reports

* China's April business sentiment rises, Caixin PMI shows

SINGAPORE, May 6 (Reuters) - Oil futures climbed on Monday after Saudi Arabia hiked June crude prices for most regions and as the prospect of a Gaza ceasefire deal appeared slim, renewing fears the Israel-Hamas conflict could still widen in the key oil producing region.

Brent crude futures gained 34 cents, or 0.4%, to $83.30 a barrel at 0518 GMT, while U.S. West Texas Intermediate crude futures were at $78.45 a barrel, up 34 cents, or 0.4%.

Saudi Arabia raised the official selling prices (OSPs) for its crude sold to Asia, Northwest Europe and the Mediterranean in June, signalling expectations of strong demand this summer.

"After falling a little more than 7.3% last week due to easing geopolitical tensions, ICE Brent has started the new trading week on a stronger footing, opening higher," ING's head of commodities research Warren Patterson said in a note.

This comes after Saudi Arabia raised June OSPs for most regions amid a tightening of supplies this quarter, he added.

In China, the world's largest crude importer, services activity remained in expansionary territory for the 16th straight month, while growth in new orders accelerated and business sentiment rose solidly, boosting hopes of a sustained economic recovery.

Last week, both futures contracts posted their steepest weekly loss in three months with Brent falling more than 7% and WTI down 6.8%, as investors weighed weak U.S. jobs data and the possible timing of a Federal Reserve interest rate cut.

The geopolitical risk premium in oil prices has also eased as talks for a Gaza ceasefire are underway.

However, prospects for a deal appeared slim on Sunday as Hamas reiterated its demand for an end to the war in exchange for the freeing of hostages, and Israeli Prime Minister Benjamin Netanyahu flatly ruled that out.

"News that Israel wants to go ahead and extend its operation into Rafah, risks derailing a potential ceasefire agreement and reigniting Middle Eastern geopolitical tensions which had appeared to be easing," IG markets analyst Tony Sycamore said.

With most of the long positions in oil cleared last week, the risks appear to be for WTI prices to rebound back towards $80 in the early part of this week, he added.

In a sign supply may tighten, U.S. energy companies cut the number of oil and natural gas rigs operating for a second week in a row last week. Oil rigs fell by seven to 499, in the biggest weekly drop since November 2023, Baker Hughes said in a report on Friday. (Reporting by Florence Tan; Editing by Sonali Paul)