Suwayda24, a network of activists in the the southern Syrian province in Suwaida, said on Sunday that the four bodies were found in an area near the border with Jordan.
"They were killed last night by Jordanian border guards," the network said, adding that gunfights were heard on Sunday in border regions.
The Jordanian state news agency quoted a military official as saying on Saturday that the smugglers were intercepted as they “illegally crossed the border from Syrian territory”.
“Rapid response forces were deployed and the rules of engagement were applied by directing fire at them, which wounded one,” the official said.
“The rest fled to the Syrian interior.”
The report described the operation as a “continuation of the efforts that the Jordanian armed forces are exerting to shield domestic and regional security from the plague of drugs”.
In pictures: the Middle East's war on drugs
It did not say what happened to the wounded man or how many others had been with him.
The official said 20,000 pills of the banned stimulant Captagon were found. The army also seized an AK-47 assault rifle, an unspecified amount of ammunition and 564 pouches of hashish each weighing 200g.
Security forces frequently conduct operations in northern Jordan to curb a regional trade in Captagon and other drugs, which are manufactured mainly in Syria and Lebanon.
Official television said on Sunday that security forces discovered another 10,000 pills of Captagon and 1kg of crystal methamphetamine hidden in a container trailer that had arrived from Syria at Nassib, the only open border crossing between the two countries.
Jordan lifted restrictions at the crossing at the end of last year as part of a rapprochement with Damascus that was brokered largely by Moscow, President Bashar Al Assad's main ally.
Regional security officials say most of the drugs, particularly Captagon, pass through Jordan to Saudi Arabia, despite massive efforts by Saudi authorities to intercept them, while a significant proportion is used in Jordan.
The border with Syria has become the main conduit for the trade since Syrian regime forces retook the area from rebels in 2018 after a deal between Russia, the US and Israel.
Jordan says pro-Iranian militias in southern Syria and the Syrian military are behind the rise in drug smuggling over the past four years.
The 2018 agreement was supposed to keep Lebanon's Hezbollah and other Iran-backed groups away from the border.
Jordanian Foreign Minister Ayman Al Safadi this month told visiting Russian Foreign Minister Sergey Lavrov that Jordan hoped Moscow would help to maintain a “minimum stability” on its border with Syria.
He was referring to the flow of narcotics from areas controlled by Assad's forces.
Mr Lavrov did not publicly mention any border issues on his trip to the kingdom.