(Reuters) - Mainstream Syrian rebels seized a border crossing with Jordan from the government on Wednesday, the leader of one of the rebel groups and a security source on the government's side said, the first time Damascus has lost it since the start of the conflict.

"It has been liberated," said Bashar al Zoubi, the leader of the Yarmouk Army, one of the mainstream rebel groups in southern Syria that was involved in the offensive. "The crossing is with us," he added, in a message sent to Reuters via Internet.

The security source said government forces had pulled out to a nearby base. "The Syrian army withdrew from the Nasib bordering crossing," the source said.

Jordan, which had been cautious about provoking a military response from President Bashar al-Assad, had previously pressured mainstream rebel groups to hold back from taking the crossing, according to Jordanian security sources.

But the mainstream groups known as The Southern Front say they have received extra military support from Assad's foreign enemies in response to an offensive launched in February by Damascus to reclaim the south, rebels say.

That support has been channeled via Jordan, a staunch ally of the United States and Gulf states including Saudi Arabia that want to see Assad gone from power.

The southwestern corner of Syria is the last notable foothold of the mainstream rebellion against Assad. Elsewhere, the mainstream groups have largely been eclipsed by jihadists, including Islamic State and the al Qaeda-linked Nusra Front.

The mainstream groups denied reports that Nusra was involved. Abu Ghiath al-Shami, the spokesman for another Southern Front group, the Alwiyat Seif al-Sham, said they had expelled the jihadists from the area.

"They wanted to take part in the operation," he told Reuters via the internet. "We ejected them."