A government spokesman in Amman said, that "the number (at the border) is 12,000, but it is increasing". Last month, he said a similar estimate by the UN was "greatly exaggerated", reports BBC online Wednesday.
About 50 to 100 refugees were being allowed into Jordan each day, with priority given to women, children, and elderly and sick people. Mass entry was unlikely because of security concerns.
Many of them are believed to have fled air strikes by Russia, which supports Syrian President Bashar al-Assad, on areas controlled by the jihadist group Islamic State (IS) in eastern Homs province and neighbouring Raqqa.
UNHCR said that Jordan had legitimate security concerns, but that they could be addressed by properly assessing each case. Jordan is hosting 633,000 of the 4.39 million Syrians registered as refugees with the UN.
The government says more than one million other Syrians are living there, BBC notes.