Ten thousand Syrian refugees have arrived in Jordan in the last 72 hours, army sources at the border have told local Jordanian media.
Jeffrey Feltman, UN under secretary-general, said on Tuesday that a record 150,000 people fled Syria this month to escape the worsening conflict now trapped in a "destructive military spiral".
He told the UN Security Council that abuses committed by President Bashar al-Assad's forces were "significantly" worse than those of the opposition, even though both could face war crimes charges.
"The humanitarian situation is becoming worse in Syria," Feltman said.
There are now 413,000 Syrian refugees in Jordan, a number the UN expects to reach 500,000 as early as the end of next month.
Four million people in the country now need humanitarian assistance. Of these, two million are internally displaced.
But Feltman said the conflict has now "led more than 900,000 people to flee to neighbouring countries, including over 150,000 this month alone".
"Even tentative steps to dialogue are struggling to take root. The destructive military spiral churns more forcefully each day and threatens to pull its neighbours, most notably and worrisomely Lebanon, into its vortex," he said.
"Regrettably, the warring parties remain locked in a military logic which is bound to bring more death and destruction."
The UN estimates that more than 70,000 people have died in the nearly two-year-old conflict.
"Both have committed abuses amounting to war crimes, although the scale of abuses committed by the government side significantly exceeds those of the opposition," Feltman said.
Meanwhile, the Washington Post reported on Tuesday that the White House was considering a shift in its policy toward the nearly two-year-long conflict in Syria.
The report, citing US and European officials, said it may send body armour and armoured vehicles to rebels, and possibly provide military training as well.
John Kerry, the US secretary of state, was expected to discuss the proposed policy change with officials during his nine-nation tour of European and Arab capitals, the newspaper said.
US officials remain opposed to sending weapons to the rebels, it said.
Kerry is to meet Syrian opposition leaders at a "Friends of Syria" conference in Rome on Thursday.
On Monday in London, Kerry said President Barack Obama was evaluating more steps to "fulfill our obligation to innocent people", but did not give details or say whether Washington was reconsidering whether to arm the rebels.
"We are determined that the Syrian oppositions is not going to be dangling in the wind," he said.