Formerly united against Islamic State, the Kurdish-led SDF and the Military Council supported by Arab tribal leaders have been fighting for several weeks.
Mozambique's President Filipe Nyusi told a news conference on Friday that Omar had been killed on Tuesday, but cautioned that the fight against the insurgency was not over.
After an attack on Iran's Parliament in 2017 which also targeted an important shrine, militants have targeted a similar site again
Islamic State, which operates sleeper cells in lands it once ruled, claimed responsibility for the attack in a statement on its Telegram channel.
Abu Hussein al-Husseini al-Quraishi took over in November 2022 after his predecessor was killed, also in Syria.
The four dead included a police colonel, officials said. Six people were also wounded.
Islamic State on Monday claimed responsibility for the suicide bombing of a political rally in Pakistan that killed at least 45 people.
Once Britain's most high-profile Islamist preacher, Choudary has been charged with three terrorism offenses after being arrested in London last week.
The Iraqi prime minister began an official visit to Syria on Sunday, for the first time since the outbreak of the Syrian war.
The suspects arrested in Germany had also been collecting money for Islamic State since April 2022 and repeatedly transferred it to the group abroad.
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