"The Russians and the Syrian regime offer no safety", he said.
Mr Assad is also aiming to recover control of rebel-held areas of Quneitra province at the frontier with the Israeli-occupied Golan Heights.
The Jordanian borders have been closed since 2015, and a Syrian military officer said the decision to reopen the crossing is a political one between both countries.
In Daraa province-the cradle of the 2011 revolt that sought to topple Assad-ferocious bombardment during the two-week assault eventually forced the militants to strike a bargain with the Russians.
The strikes were aimed at taking back territory lost to insurgents in recent years.
An exit route for those who wish to relocate to Idlib will also be opened as part of the agreement, keeping with the terms of previous deals between the government and rebels.
Footage posted on social media of women and children pleading with King Abdullah to let them in has generated a wave of sympathy in Jordan with the plight of the newly displaced Syrians.
The collapse of rebel resistance in southwestern Syria leaves only two significant areas beyond the regime's (and therefore Russian) control.
In addition to ending the Syrian military offensive the deal also calls for the gradual withdrawal of Syrian Army forces from the towns they've taken, to be replaced by local forces who are overseen by Russian Federation. "The war and more fighting won't stop the struggles of the Syrian people". Witnesses said they left the border for different parts of Deraa province where fighting has died down.
Regarding the operation which resulted in establishing control over the Radar Battalion, another field commander said that as soon as the army established control over al-Nu'aima, preparations to storm the Battalion from several directions began, killing numerous terrorists who had barricaded themselves inside it.
Most of the hospitals had shut down amid the destruction in insurgent territory, which now barely had access to water or electricity, he said.
The Russia-backed regime offensive has displaced around 320,000 people since June 19, the United Nations says, including tens of thousands who fled south to the sealed border with Jordan.
US forces have backed rebels fighting Assad's government during the civil war.
Lebanon's Iran-backed Hezbollah is helping to lead the offensive in south Syria but keeping a low profile, pro-Damascus sources have said, in defiance of Israeli demands.
Hours after opposition factions signed onto Friday's reconciliation agreement, SAA soldiers and armored vehicles entered the Naseeb border crossing along the Syrian-Jordanian border on Saturday, where upwards of 100,000 displaced Syrians from across Daraa's eastern countryside had gathered.