The cars were forced to turn back but a short while later a pick-up truck and two motorcycles returned in the direction of the Jordanian border, the statement said.
The guards opened fire, killing five people and destroying their vehicles, it said.
In a separate incident, two other people were arrested for trying to cross the border from Syria illegally, the army said.
The statement provided no further details about the incident or the identities of those killed.
On June 3, border guards foiled an attack also on the frontier with Syria and killed gunmen riding motorcycles who tried to overrun their positions.
It said the armed men on motorcycles, who belonged to "terrorist groups and coming from Syria", tried to attack the border guards at the Rukban border crossing on the Jordanian side of the frontier.
In June last year, a suicide bombing claimed by the Islamic State jihadist group killed seven soldiers in a no-man's land near the Rukban crossing.
Soon after the attack, the army declared Jordan's desert regions that stretch northeast to Syria and east to Iraq "closed military zones".
Jordan is part of the US-led coalition fighting IS.
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The guards opened fire, killing five people and destroying their vehicles, it said.
In a separate incident, two other people were arrested for trying to cross the border from Syria illegally, the army said.
The statement provided no further details about the incident or the identities of those killed.
On June 3, border guards foiled an attack also on the frontier with Syria and killed gunmen riding motorcycles who tried to overrun their positions.
It said the armed men on motorcycles, who belonged to "terrorist groups and coming from Syria", tried to attack the border guards at the Rukban border crossing on the Jordanian side of the frontier.
In June last year, a suicide bombing claimed by the Islamic State jihadist group killed seven soldiers in a no-man's land near the Rukban crossing.
Soon after the attack, the army declared Jordan's desert regions that stretch northeast to Syria and east to Iraq "closed military zones".
Jordan is part of the US-led coalition fighting IS.
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