"We want it to be an operation in which everyone says they have taken revenge on the Americans," Abu Alaa al-Walae said.
In the absence of the ability to remove them, airstrikes against Iranian weapons trafficking and its drone bases amount to the only way to keep Tehran in check.
Moscow has repeatedly hinted it could send some of its most advanced air defense systems to Syria.
Jones, who was married to British Jihadi Junaid Hussain, was said to have been killed near the Syria-Iraq border.
At least 13 others were wounded in a suspected drone strike targeting ISIS.
The group may now use guerrilla warfare and turn its attention to attacking civilian targets.
An internal memo said the U.S. must threaten military strikes to deter Assad.
The Al-Qaeda affiliated group are launching daily attacks in Somalia.
Just three months in, 2016 is already the deadliest year for U.S. attacks on the militant group.
The Pentagon claimed to have killed 150 militants in strikes on an Al-Shabab training camp.
A U.S.-led coalition has killed 10 Islamic State leaders in the past month.
U.S. Defense Secretary Ash Carter says he expressed condolences to Iraq's premier.