The al-Qaida organisation in the Arab Peninsula said it would start targeting Saudi forces if they continued to hunt down Islamist members.
Published on an Islamist website on Wednesday, the statement said Hajj was on an undisclosed mission when he was ambushed and killed by security forces in the Saudi capital Riyadh.
A Yemeni national, Hajj is believed to have once acted as a bodyguard of al-Qaida leader Usama bin Ladin.
The statement said he had been on "missions" in Afghanistan, Europe and south-east Asia.
But he was killed along with suspected Islamist fighter Ibrahim al-Muzaini when security forces opened fire on their vehicle.
Newspaper pictures showed their bodies still slumped in the front seats.
"Their murder will only fuel our determination and enthusiasm to avenge them," the statement said.
"We warn members of the security, emergency and intelligence forces not to confront the mujahidin because it will be very easy to attack you in your homes or workplace, but this is not part of the mujahidin's policy now."
Attacks in Saudi Arabia have so far focused on foreign targets, particularly expatriate residential compounds.
Last year more than 50 people were killed in bombings of compounds in May and November.
In December fighters tried at least twice to assassinate senior Interior Ministry officials in the first sign they might change tactics.
An undated handout
of Khalid Hajj
Hajj had been wanted by Saudi authorities since May for that month's triple bombing - blamed on al-Qaida - which killed at least 35 people in Riyadh, including nine Americans.
Saudi-owned al-Sharq al-Awsat daily reported on Wednesday that Abd al-Aziz al-Muqrin has taken Hajj's place as leader of al-Qaida cells in Saudi Arabia.
Muqrin is the suspected mastermind of the November attack and one of the kingdom's most wanted fugitives.