By Yuka Obayashi

TOKYO (Reuters) - Oil prices rose in early Asian trading on Monday on concern over tighter global supply brought about by escalating conflict in the Middle East and between Russia and Ukraine, while a shrinking U.S. rig count added to upward price pressure.

futures had climbed 24 cents, or 0.3%, to $85.67 a barrel at 0029 GMT. futures gained 25 cents, or 0.3%, to $80.88 per barrel. Both benchmarks logged less a than 1% change last week versus the previous week.

"Escalating geopolitical tension, coupled with a rise in attacks on energy facilities in Russia and Ukraine, alongside receding ceasefire hopes in the Middle East, raised concern over global oil supply," said Hiroyuki Kikukawa, president of NS Trading, a unit of Nissan (OTC:) Securities.

"Falling U.S. rig count also increased worry over tighter supply," he said.

Russia struck critical infrastructure in Ukraine's western region of Lviv with missiles early on Sunday, Kyiv said, in a major air strike that saw one Russian cruise missile briefly fly into Polish airspace, according to Warsaw.

Moscow launched 57 missiles and drones in the attack that also targeted the capital Kyiv, two days after the largest aerial bombardment of Ukraine's energy system in more than two years of full-scale war, Kyiv said.

The move follows Ukraine's recent attacks on Russian oil infrastructure, with at least seven refineries targeted by drones just this month.

In the Middle East, Israeli forces besieged two more Gaza hospitals on Sunday, pinning down medical teams under heavy gunfire, the Palestinian Red Crescent said. Israel said it had captured 480 militants in continued clashes at Gaza's main Al Shifa hospital.

U.S. Secretary of State Antony Blinken told Israeli Prime Minister Benjamin Netanyahu on Friday that Israel risked global isolation if it attacks the Palestinian city of Rafah in the Gaza Strip.

Meanwhile, the U.S. oil rig count fell by one to 509 last week, showed data from energy services firm Baker Hughes, indicating lower future supply.