"We will kill anyone, whether Arab, foreign or Iraqi, inside any truck carrying goods to the occupation forces," said a statement from the leadership of the resistance movement in Ramadi, west of Baghdad.
"We will also kill anyone providing intelligence or information to the occupation forces. We will, however, reward anyone who informs us of such traitors.
"As such, we warn Jordanians not to collaborate with the forces of the occupation in the future, and if they do, then they have only themselves to blame," said the statement.
Four Jordanians were taken hostage on 27 July by a group calling itself the Death Squad of Iraqi Resistance.
They were released in Falluja on Wednesday after the Shura council, a consultative religious body, negotiated their release.
The previously unheard of group used a videotaped message sent to Aljazeera to urge the Jordanian people to pressure Amman to end its support of the US-led occupation of Iraq.
Jordanians released, warned
A spokesman for the foreign ministry in Amman confirmed their release, adding that no concessions had been made.
The Iraqi mediator also called the resistance group "criminals", adding the Jordanians were freed because the council ruled they were innocent.
Supply convoys are an easy
target for resistance groups
But the council issued a statement saying the release of the men should be a message to all Jordanians to remind them of the religious and ethnic bonds that tie them to Iraqis.
At least 23 captives, most of whom are truck drivers from Turkey, Kenya and India, are being held by different groups in Iraq.
The demands are that their employers stop working with the US-led occupation forces in Iraq and the US-appointed interim Iraqi administration.
Two Indian truck drivers who worked for Kuwaiti transport firms, Harnak Singh, 30, and Tarlok Singh, 43, claimed that US forces would abandon them when the trucks they were driving came under sustained attack.
The truck drivers would then be left to fend for themselves, they claimed.
They said the Iraqi resistance believes the US-led occupation would falter if its supplies were cut. This would force the Americans to leave, they said.