Mohamed Momani, who is also Jordan's information minister, said "around 16,000 Syrians are located in camps situated a few hundred metres from the Jordanian side (of the border) in no-man's land."
The UN said in December that 12,000 Syrians were stranded on the border and urged Jordan to take them in, but Momani at the time dismissed the report as exaggerated.
On Monday, he told AFP in written remarks that the refugees were receiving humanitarian assistance from Jordan as well as the UN and aid organisations.
Jordan says it is hosting 1.4 million Syrian refugees who have fled the now nearly five-year war across the border, while the UN refugee agency UNHCR puts the number at 600,000.
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During the first two years of the Syrian conflict, 45 crossing points were open along the 378-kilometre (235 mile) frontier.
There are now only two open, with the UNHCR saying they are located in rocky desert areas, devoid of water, shade or vegetation.
"Jordan's security is the first priority for the kingdom, nevertheless our borders remain open," said Momani.
He said the 1.4 million Syrian refugees present in Jordan represent 20 percent of the country's total population.
Jordan receives "up to 5,000 refugees per day at times. This has been mostly done at Jordan's expense," he added.
The kingdom has repeatedly said that the influx of refugees is a burden that has strained its already poor resources in water and electricity and urged more help from the international community.
"Jordan encourages international agencies to provide all the needed support," he added.
Syria's war has killed more than 260,000 people and forced millions from their homes.