Speaking at a press conference in Karak, Major General Abdallah al-Maaytah said most of those wounded in the shooting at the Hamoud Church in Karak were still receiving treatment, and that the hunt for the attackers was ongoing.
Interior Minister Mazin Al Farrayeh said the attack had been carried out by "extremists", but that it was too early to tell whether they had any links to known groups either inside or outside Jordan.
There was no immediate claim of responsibility.
A video aired on Jordan's state-owned Al-Mamlaka television station that appeared to be from a security camera mounted on the church showed three people firing at it from a sidewalk and hiding behind trees and a low wall. The video showed the attackers then running towards the church's entrance.
Reuters was able to verify the video from the entry path and wall surrounding the church, as well as other details.
Khaled Burqan, who was at the funeral, told Al-Mamlaka that dozens of people were present and that the gunmen opened fire on them for several minutes.
Ihab Ammareen, another witness, told the station that he saw bloodied people collapse on the floor after the attack. "People were crying, wailing, screaming — it's hard to describe," he told the station.
Jordan's King Abdullah visited Karak hours after the attack and said the perpetrators would be punished "with an iron fist".
"The terrorist attack against Karak will be met with the harshest retaliation. Those who delude themselves into thinking that they can divide Jordanians with their bullets have no chance in the face of our unity," he said in a statement.
Reuters footage from the church after the attack showed blood smeared on the floor near its entrance, where security forces were deployed.
Such attacks are extremely rare in Jordan, which is relatively stable, though Jordanian authorities say they have repeatedly foiled attempted attacks by Islamist militants in recent years.
Christians make up a minority of Jordan's population. The country is home to several biblical sites that attract Christian pilgrims from around the world.
Jordan's Minister of Endowments and Islamic Affairs Mohammad Khalayleh and several members of Jordan's parliament condemned the attack in comments to Al-Mamlaka.
The US ambassador to the United Nations Mike Waltz described it in a post on X as a "depraved and brutal attack on a house of worship."
Jordan was among the US allies in the region to be hit by Iranian attacks this year after the US and Israel launched strikes against Iran in February.
