Since the start of September, 24 men wanted in drug cases have been arrested, authorities said on Wednesday.
The kingdom is fighting a drug war on the 360km border with Syria, through which flows billions of dollars worth of narcotics a year and on to the Arabian Peninsula.
“The smuggling of drugs from Syria to Jordan is a big challenge,” Mr Safadi said in Amman.
“We are continuing to confront this danger with all our capabilities and we will continue to do what is needed to defeat this danger and protect our society and country.”
The flows mainly comprise the amphetamine pill known as Captagon, which is cheap to manufacture.
Jordan has accused the Syrian military and pro-Iranian militias allied with it of sponsoring the trafficking of the drug.
Large areas in southern Syria returned to the hands of the military in 2018 after a deal between Russia, Damascus's most powerful supporter, the US and Israel to hand them over to President Bashar Al Assad's forces.
In an interview last month, Mr Al Assad denied the state's involvement in the trade and blamed neighbouring countries he did not name for fostering the trafficking.
In July, Syrian and Jordanian security officials met in Amman to discuss the issue.
In the last two years, the Jordanian military has been engaging more forcefully with the smugglers. The US and other western allies have supported the efforts by building surveillance and monitoring systems on the frontier.
Jordanian authorities have also increased operations inside the kingdom to halt the domestic consumption of the drugs.
Since the beginning of September, authorities have arrested 24 men wanted in drug cases. A police spokesman described them as “threats to society” when announcing the arrests on Wednesday.
One of the most dangerous smugglers was arrested in the northern Badia region, which borders Syria, he said. The bust also netted 4,000 drug pills and 30 pouches of hashish.
In the southern governorate of Aqaba, Jordan's only sea outlet, security forces overran the tent of another dealer, where he had stored 15,000 pills, 17 pouches of hashish and an automatic weapon, the spokesman said.
The remaining smugglers were arrested in Zarqa and Balqa governorates, adjacent to Amman, and in the governorates of Irbid and Ramtha, which border Syria.