In response to the strike, Syria said it had closed a border crossing with Jordan.
"The decision includes the complete suspension of passenger and commercial traffic in both directions, to ensure the safety of travellers and workers at the crossing," Syrian authorities said in a statement carried by state media.
It added that it had "opened direct channels of communication" with Jordanian officials and had launched "comprehensive investigations to establish the full circumstances of the targeting".
Nassib is the only passenger and commercial border crossing between Jordan and Syria.
Earlier on Monday, senior government security officials said Jordanian security forces had arrested two brothers and their brother-in-law over the church attack.
The Public Security Directorate (PSD) said the unnamed "terrorists" were found hiding in an abandoned house in Karak before dawn.
Jordan's Interior Minister Mazen al-Faraya told state-affiliated TV the attackers were all Jordanians and "had been holed up in a building in one of the villages near the site of the attack".