Update: There are unconfirmed reports that US aircraft have attacked Iranian positions near the eastern Syrian city of Al-Bukamal.

There are unconfirmed reports from Iranian sources that U.S. aircraft have attacked Iranian positions near the eastern Syrian city of Al-Bukamal. — Evan Kohlmann (@IntelTweet) January 4, 2020

Fire can be seen in the distance after reports of airstrikes near Al-Bukamal and #Iraq pic.twitter.com/qJQiMigpzN — Strategic Sentinel (@StratSentinel) January 4, 2020

Meanwhile, a US surveillance drone was reportedly shot down by Iran's Popular Mobilization Forces (PMF) in Anbar, however there has been no official confirmation.

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Summary:

Multiple 'Katyusha' unguided missiles/mortars fired into two regions near Baghdad.

Green Zone neighborhood in Baghdad, comes under mortar shell attack: 5 ppl wounded.

Balad airbase (hosts US troops) near Baghdad hit by missiles: 3 Iraqi soldiers wounded.

Explosion heard at Al-Kindi base in Mosul (which houses US troops): no details on injuries yet

Hezbollah warns Iraqi Security Forces to stay away from US bases.

Iraqi Kata'ib Hezbollah warning Iraqi Security Forces should stay away from US bases starting Sunday evening. pic.twitter.com/inW1zDgZMU — Aldin 🇧🇦 (@aldin_ww) January 4, 2020

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As 1000s march in the streets of Baghdad to moutn the death of Soleimani, Al-Arabiya (and other local news sources) report rockets have landed in the heavily fortified Green Zone in Baghdad, where the US Embassy (among other things) is located.

Witnesses told Reuters that an explosion was heard in the Iraqi capital, Baghdad

شهود لرويترز: سماع دوي انفجار في العاصمة العراقية بغداد — سكاي نيوز عربية-عاجل (@SkyNewsArabia_B) January 4, 2020

Sky News Arabia reports that the missile landed in the Green Zone in Baghdad and closed the entrance to the road leading to the American embassy.

مراسلنا: سقوط صاروخ على المنطقة الخضراء في بغداد وإغلاق مدخل الطريق المؤدي إلى السفارة الأميركية — سكاي نيوز عربية-عاجل (@SkyNewsArabia_B) January 4, 2020

An unguided 'Katyusha' rocket was reportedly launched...

Iraqi police sources: A Katyusha rocket landed inside the Green Zone [near the US Embassy] in Baghdad. pic.twitter.com/7ybzDMlNy9 — Hamoud_Mohammed (@news_hamoud) January 4, 2020

Dozens of US Apache helicopters are now seen overhead...

#BREAKING

Numerous U.S. helicopters in the air over #Baghdad, #Iraq.

After Rocket hits Baghdad's Green Zone. Entrance to the U.S. Embassy remains closed. pic.twitter.com/uEjA5irrve — News flash (@BRNewsFlash) January 4, 2020

President Rouhani reportedly threatened a "lightning strike" against America...

Additionally, there are now reports that multiple rockets have struck Balad Airbase, located just north of Baghdad, that hosts US troops...

A third mortar attack is reportedly underway at the US military base at Al-Kindi in Mosul...

#Update: Picture of inside the military base of Al-Kindi in #Mosul in #Kurdistan in #Iraq now being reported about 10 mortars hit inside the compound and around the compound. Reports also suggest that a number of #US troops are located at the base.#Iran pic.twitter.com/KWEnTb8Am5 — Sotiri Dimpinoudis (@sotiridi) January 4, 2020

Meanwhile, Iraqi police have opened fire at armed PMU militiamen during the funeral procession.