Oil prices fell Monday as Israel stepped up ground attacks on Hamas targets in Gaza but held back from a full-on incursion, fanning hopes a wider conflict can be avoided.

However, equities were in the red ahead of a Federal Reserve policy meeting this week, with traders fearing it will likely keep interest rates elevated for an extended period as inflation remains stubbornly high.

Crude pared Friday's almost three percent gains as Israel's military continued air and ground operations in Gaza, though it took a more cautious approach than feared.

Instead of a broad offensive, officials have opted for targeted attacks on a day-to-day basis, tempering worries of an all-out war that could drag on Iran and even the United States.

The White House urged Israel to protect innocent Palestinians in Gaza by distinguishing between Hamas militants and civilians, while the United Nations warned that "civil order" was starting to collapse in the territory.

Thousands of civilians have been killed on both sides since the conflict was triggered by an unprecedented attack on Israel by Hamas on 7 October.

The threat of a wider conflict remains, with Iran saying the battle could "force everyone to take action", while US National Security Advisor Jake Sullivan said there was an "elevated risk" of a spillover.

But observers said there was a sense of relief among investors for now, easing crude supply worries and taking some pressure off prices.

"The weekend showed the armed conflict remains limited to Israel and Gaza — in that light, crude looked overbought," Vandana Hari, of Vanda Insights, said.

Crude will "likely continue sliding until the next risk event".

Still, equity markets struggled to build on Friday's rally in Asia, tracking losses in the S&P 500 and Dow.

Tokyo sank more than one percent, while Hong Kong, Shanghai, Sydney, Singapore, Taipei, and Wellington were in the red, though Seoul and Jakarta eked out gains.