On the opposition side, the Syrian Observatory for Human Rights said the government has become in control over 72.4 percent of Daraa while the rebels' control has shrunk to 21 percent, adding that a rebel group allied with the Islamic State (IS) controls 6.6 percent of Daraa.
There was no immediate comment from Jordan on the Syrian forces' recapture of the Naseeb crossing.
The border assault of the past two weeks has created a new problem for Jordan in the shape of tens of thousands of civilians who have fled intensive aerial bombardment of their towns and moved towards the border.
Under the agreement, Syrian forces will not be allowed to remain in the area re-taken by the government, sources told Al Jazeera.
"An agreement has been reached between the Syrian government and the terrorist groups" that includes "the handover of heavy and medium weapons in all cities and towns", the official SANA news agency said. "We have ended their existence", he said of the rebels. The first group of 400 headed back to Syria a week ago.
An agreement reached Friday may offer a glimmer of hope in a fast-deteriorating situation in southwestern Syria, where at least 330,000 people - half of them children - have fled their homes in the face of a fierce regime offensive.
USA forces have backed rebels fighting Assad's government during the civil war.
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Waves of air strikes pounded rebel-held areas of southern Syria on Thursday as pro-regime forces unleashed their most intensive bombing campaign yet in a two-week-old offensive.
Syrian government forces now control all the towns and villages on the eastern side of Daraa province, including the villages of Nuaima and Saida, which sits 10 kilometers ahead of the Naseeb crossing and links the eastern and western sides of Daraa.
The rebels who support the deal and want to stay in their towns can stay, while the ones who refused to reconcile can leave Daraa toward rebel-held areas in Idlib province in northwestern Syria.
The United Nations has called on Jordan to open its border.
He said the worldwide community should support Jordan and warned that thousands of lives would be lost if urgent action was not taken.
Seven years into the war which has killed hundreds of thousands of people, Assad now commands most of Syria with his allies' help, though most of the north and a chunk of the east remains out of his hands.
Southwest Syria is a "de-escalation zone" agreed previous year by Russia, Jordan and the United States to reduce violence.