An estimated number of 4,000 Syrians at Hadalat and 45,000 Syrians at Rukban - mainly women and children - remain stranded at Syria's southern border with Jordan, the statement said.
Leaving the area risks danger and deprivation in an "inhospitable desert location", making many Syrians "unsure of where to go in search of safety". The refugees stuck at the Hadalat border crossing were reportedly living exclusively on flour and water, he added.
The UN reports on the thousands of women, men and children who gathered on the border between Jordan and Syria.
A suicide bombing claimed by the Islamic State jihadist group in June a year ago killed seven Jordanian soldiers in no-man's land near the Rukban border crossing. Since then, global aid organizations have wrestled with the dilemma posed by sending aid to an off-limits area.
Jordan is part of the US-led coalition fighting IS. With the help and coordination of several United Nations agencies, the worldwide community is continuing to support daily life of the refugees and to assist Jordanian authorities in provide protection and additional life-saving assistance as needed.
The Syrian army recently advanced to the border with Jordan for the first time since 2011 - when foreign-backed militancy started in Syria - liberating a 30-kilometer-long stretch of land along the frontier.
The UN has called on all sides "take the necessary steps to prevent further harm to the frightened and highly vulnerable individuals stranded at the border", Haq said. It also said the capture closed major smuggling points used by rebels to bring weapons and fighters from Jordan into the war-torn country.
Jordan shares a desert border of more than 370 kilometers with Syria and says it is hosting 1.3 million Syrian refugees. Jordanian authorities voiced their concern over Iran's expanding influence in Syria.