"The world is not going to allow them to get away with this," al-Jubeir said, referring to Assad's army and his military allies, which include Russia and Iran.
The US and Saudi top diplomats were in the Swiss city to salvage Syria's crumbling truce, as well as the peace talks that depend on it.
"Bashar al-Assad's days are numbered," al-Jubeir said to a few reporters ahead of his meeting with Kerry, according to Qatari broadcaster Al Jazeera.
"He can leave through a political process, which we hope he will do, or he will be removed by force," he added.
Saudi Arabia has been one of the most important backers of the Syrian opposition, including armed groups, and it hosts the main opposition bloc that has taken part in the Geneva peace talks.
The recent surge in Syria's violence, especially in the northern city of Aleppo, has scuttled a US-Russian ceasefire that went into effect in most parts of the country in late February.
"We look for Russia's cooperation" to get the Syrian army to halt fighting, Kerry said on Sunday in Geneva, referring to Moscow's influence with Syria.
Kerry said there were constant diplomatic contacts with Russia, but a diplomatic source told DPA that there was currently no plan for Kerry and Russian Foreign Minister Sergei Lavrov to meet in the next few days.
Syria's government said on Sunday it was extending a ceasefire in and around Damascus, while activists reported heavy fighting by the regime and rebels in Aleppo.
The temporary ceasefire excludes Aleppo, where rebels on Sunday fired shells on regime-held areas and unidentified helicopters dropped barrel bombs on rebel-controlled areas.
Kerry was also scheduled to meet UN Syria mediator Staffan de Mistura in Geneva on Monday.
De Mistura said last week that there should be a meeting of foreign ministers from the US, Russia and influential Middle Eastern countries to salvage the truce and the fledgling peace process.
New raids hit Aleppo
Fresh air strikes hit Syria's Aleppo city early Monday, an AFP correspondent said.
More than a week of fighting in and around Syria's second city has killed hundreds of civilians.
Heavy air strikes hit rebel-held east Aleppo in the early hours of Monday, AFP's correspondent there said, but there were no immediate reports of casualties.
Several neighbourhoods, including the heavily populated Bustan al-Qasr district, were struck. It was not clear if Syrian or Russian jets carried out Monday's raids on the rebel-held area.
Rebel shelling of government-controlled western areas of Aleppo city late Sunday killed three civilians including a child, the Syrian Observatory for Human Rights said.
Growing violence in and around Aleppo has killed more than 250 civilians and threatened both a UN-backed peace process and a fragile ceasefire.
