Calls for their withdrawal increased after the group was defeated in 2017. The militia group's website published only al-Muhandis' statement on Thursday.
In a marked escalation in rhetoric, the Brigades issued a fiery statement later Thursday warning the USA that any new attack on an Iraqi position will be met with a harsh response.
"Be sure that if the confrontation between us starts, it will only end with your removal from the region once and for all", it said. The official spoke on condition of anonymity because of the sensitivity of the subject.
He said the attacks were carried out by "agents or in special operations with modern airplanes", without providing further details. Iranian media reported a funeral for a "shrine defender" named Abolfazl Sarabian on the next day, which typically denotes someone fighting in Iraq and Syria.
The statements by al-Fayyadh and al-Muhandis followed at least three mysterious explosions at militia bases and munitions depot around Iraq over the past month, including a massive blast near Baghdad that killed one civilian and wounded 28 on August 12. The base housed a weapons depot for the Iraqi federal police and the PMF.
Al-Fayyadh's statement alleged the attacks on the bases over the past weeks "were the result of an act organized by a foreign side", but refrained from naming that side.
Israeli Prime Minister Benjamin Netanyahu has hinted that his country was behind the latest attacks on ammunition depots in Iraq belonging to the Iran-backed Popular Mobilization Forces (PMF).
In an interview with a Russian-language TV station Thursday, Netanyahu indicated the speculation is true.
"We act in many arenas against a country that desires to annihilate us", he said in response whether Israel operates in Iraq. Obviously, I've given the security forces the order and the operational freedom to do what is necessary to disrupt these plots by Iran", Netanyahu reiterated, adding, "And obviously I've also led, and in many ways continue to lead, a global effort against Iran.
USA officials said Israel was responsible for the bombing of an Iranian weapons depot in Iraq last month, airstrikes which would mark a significant escalation in the campaign against Tehran's military entrenchment across the Middle East.
Israel says it has carried out hundreds of strikes in Syria, some of them against Iranian targets, to prevent Teheran from establishing a permanent military presence there and to stop advanced weapons reaching its proxies in the area. Though Israel has maintained an official policy of non-intervention in the Syrian civil war and often remained silent in the face of air strike accusations, in January then Chief of Staff of the Israeli army Gadi Eisenkot admitted Israel had in fact struck Syria "thousands of times".