The embattled regime of Syrian President Bashar al-Assad is not close to falling despite nearly two years of fighting between government forces and rebels seeking to depose him, Jordan's King Abdullah II said Friday.

"Anyone who says that Bashar's regime has got weeks to live really doesn't know the reality on the ground," he said during a panel appearance with CNN's Fareed Zakaria at the World Economic Forum in Davos, Switzerland.

"They still have capability. ... So (I expect) a strong showing for at least the first half of 2013."

Nonetheless, fears are growing that Syria may implode as the protracted conflict gets nastier.

Any fragmentation of the country into small states would be "catastrophic and something that we would be reeling from for decades to come," Abdullah said.

He also warned of the threat of foreign jihadist fighters now in Syria.

Al Qaeda has been established there for the past year and is getting support "from certain quarters," the king said.

"They are a force to contend with, so even if we got the best government into Damascus tomorrow, we have at least two or three years of securing our borders from them coming across and to clean them up," he said.

Comparing the militant threat with that seen in Afghanistan, Abdullah said that "the new Taliban that we are going to have to deal with will be in Syria."

Abdullah appealed for greater international help for more than 300,000 Syrian refugees who have already fled over the border into Jordan and are suffering in the grip of a cruel winter.

He also urged the stockpiling of humanitarian supplies that could be taken across Syria's borders, to try to keep people from leaving -- and to win hearts and minds.

"If these people start to starve and they don't have fuel and electricity and water, and hospitals are not running, that's when radicalization comes in and take advantage," he said.

The number of Syrians fleeing to a Jordanian desert in the dead of the night continues to skyrocket, as officials warn of dwindling resources and a prolonged humanitarian crisis.

About 3,280 Syrians crossed into the Zaatari refugee camp overnight on Thursday, said Anmar Hmoud, a Jordan government spokesman for Syrian refugee affairs.

A day earlier, nearly 3,000 refugees arrived in Jordan, according to the United Nations High Commissioner for Refugees.

"Indicators show they keep coming and it's much more than we're used to," Hmoud said.

As many as 36,000 Syrians have crossed into Jordan since January 1.

And as more people take refuge from the upheaval, the escalating numbers are straining resources, officials said.

About 350,000 Syrian refugees have fled to Jordan since the conflict began, a number described as "staggering" by Jordanian Foreign Minister Nasser Judeh.

"The weakest refugees are struggling now just to survive this year's harsh winter," Abdullah said. "More international support is desperately needed.