The Mahdi Army, al-Sadr's own force, is concentrated in both the areas.
Al-Sadr also accused the Iraqi government of being too close to the US military.
"The occupation has made us target of its planes, tanks, air strikes and snipers. Without our support this government would not have been formed," he said.
"But with its alliance with the occupier [the Iraqi government] is not independent and sovereign as we would like it to be."
Iraqi security forces moved against Shia militia groups in Basra on March 25, on the order of Nuri al-Maliki, Iraq's prime minister, himself a Shia.
US and British forces gave reconnaissance and tactical support to the Iraqi military during the crackdown, which triggered clashes across Shia areas of Iraq, including Sadr City, al-Sadr's stronghold.
Although al-Sadr called his Mahdi Army fighters off the streets of Basra soon after the violence, raids by government forces have continued.
Hundreds of people have been killed and wounded since the operation.
Right groups criticised
At least 13 people were killed and 80 injured in Sadr City on Saturday, while Iraqi troops took control of a northern district of Basra.
Troops entered the Hayaniya district of Basra and took control after several hours, Major-General Abdel Karim Khalaf, an interior ministry spokesman, said.
"We launched an operation in the morning. There was some exchange of fire. The operation is now over in Hayaniya without any strong resistance," he said.
Al-Sadr also criticised human right groups in his statement on Saturday.
He said: "Gaza was surrounded and everybody kept quiet. And now it is [Sadr] City and Basra and everybody is quiet.
"Where are the human rights. Where are the laws you want to adopt for freedom and democracy?"
The Iraqi and US military are building a security wall through Sadr City.
The barrier is aimed at stopping fighters from firing rockets towards the capital's heavily fortified Green Zone, where the government and US embassy is situated.