The crowd called for the expulsion of remaining American forces from Iraq during the demonstration commemorating the 2020 air strike that killed Soleimani and his lieutenant Muhandis.
Both General Qasem Soleimani, the head of Iran's Quds force and Abu Mahdi al Muhandis , deputy commander of Iraq's Popular Mobilization Forces (PMF) were killed in the US airstrike near Baghdad's international airport last year.
Iran’s state TV reports the country has unveiled two new missiles, as the US heads to the UN to trigger snapback sanctions after the Security Council rejected Washington's bid to extend Tehran's arms embargo.
Protesters were angry at what they describe as insulting coverage of Muhandis, the late leader of the Popular Mobilisation Forces, by MBC channel.
The assault sent warning sirens blaring across the diplomatic compound but it was unclear exactly what was hit and how many rockets made impact.
Qatari Emir Sheikh Tamim bin Hamad Al-Thani held talks with Iran's President Hassan Rouhani in Tehran.
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