Most stock markets rose Monday as oil prices tumbled after Donald Trump announced an "energy ceasefire" between Russia and Ukraine, which offset a fresh wave of Houthi attacks on Saudi Arabia.

Both main crude contracts sank more than one percent following the US president's declaration, even as it sparked astonishment in Kyiv, which also said Moscow had struck multiple power plants in the country.

"Effective immediately, there is an ENERGY CEASEFIRE in the War between Russia and Ukraine," Trump said early Sunday on Truth Social. "Both parties have agreed. Do not break it!"

His post came after he called on Ukrainian President Volodymyr Zelensky to halt attacks on Russian refineries and said it was "time for Ukraine to get a new president" who would finally settle the war.

Zelensky appeared to express surprise at the announcement, saying he was seeking further details, but added that "Ukraine supports the ceasefire, and it is important that Russia support it as well".

Russia has yet to confirm its agreement.

While the announcement was welcomed by Ukraine's allies, Trump had come under fire after declaring a temporary easing of US sanctions on Russian diesel, which European leaders and Kyiv said would only embolden Russian President Vladimir Putin.

The drop in oil prices reversed an initial spike that came in response to Houthi attacks on Saudi Arabia at the weekend.

At least a dozen people were killed at Riyadh's international airport Saturday -- the deadliest attack on Saudi soil for more than a decade -- and another one died following a second strike on Sunday.

The assaults marked a sharp escalation in the Yemen war, where Riyadh has long militarily supported the internationally recognised government against the Houthis.

The Iran-backed group on Sunday claimed multiple attacks over the past 24 hours and threatened to keep targeting the kingdom's transit hubs, calling them "a theatre of operations for our forces".

"The market is no longer paying full geopolitical premium on every headline, and that is probably the most useful signal in the morning price action," wrote SPI Asset Management's Stephen Innes.

"A strike matters if it threatens real barrels, shipping lanes, refining capacity or insurance costs; otherwise, the market is getting increasingly reluctant to pay up simply because the geopolitical ticker flashes red.

"The physical market remains tight enough to keep Brent above $100, but futures are refusing to treat every new escalation as the start of another straight-line inflation shock."

The drop in oil prices provided support to most Asian markets, with Hong Kong, Sydney, Singapore, Wellington and Manila all up.

But Seoul and Taipei were dragged by losses in chipmakers SK hynix, Samsung and TSMC. Tokyo was closed for a holiday.

US futures were sharply higher.

Investors are also gearing up for the release of key US inflation and retail sales data, which could play a big role in the Federal Reserve's decision-making regarding interest rates. The bank is due to meet at the end of October.

Also in view is the beginning of earnings season this week, with banking giants JP Morgan, Goldman Sachs and Bank of America due to report.

Tech giants will follow later in the month and November, with traders keen to get an idea on the outlook for the AI sector in light of the vast sums of cash pumped into it in recent years.