Hospitals in Sadr City said they had received four bodies and treated 51 wounded by Friday morning, but gave no further casualty figures after that. Children were among the wounded.
Fighting has raged in Baghdad since Nuri al-Maliki, the Iraqi prime minister, ordered a crackdown on fighters in late March.
Several hundred people have been killed since then and while al-Maliki said the crackdown was to disarm groups of fighters, al-Sadr's followers see it as an attempt to sideline them ahead of local elections in October.
'Silence from Najaf'
Speaking at Friday prayers, Sheikh Sattar Battat, an aide to al-Sadr, said he was "surprised" that al-Sistani had failed to condemn the violence.
"We are surprised by the silence in Najaf where the highest Shiite religious authority is based," he said, referring to al-Sistani.
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"For 50 days Sadr City is being bombed ... Children, women and old people are being killed by all kinds of US weapons, and Najaf remains silent."
Battat said the al-Sadr movement has not seen any "reaction or fatwa [religious decree] from Najaf" criticising the government assault on Shia fighters in Sadr City.
"For us this means that Najaf accepts the massacre in Sadr City," he said.
Shia clerics, including al-Sistani, have remained silent despite the high numbers of people killed since al-Maliki ordered the crackdown.
Also on Friday, fighters launched rockets towards the fortified Green Zone, taking advantage of a sandstorm that gave cover from attacks by US aircraft.
US forces did not confirm any strikes inside the Green Zone but one rocket damaged the bureau of the BBC.