"I call on our neighbour Kuwait to ask that American and other bases be removed so that this state may stand hand in hand with us to remove the big nightmare and great Satan from Iraq, whose people are suffering from the occupation," Sadr said in a statement, made available to Aljazeera.
"You cannot keep silent about these crimes and you must help your brothers by removing terrorism from your land," said the statement written in Arabic.
It said Kuwait, which borders Iraq to the south, no longer needed US troops now that Saddam Hussein had been ousted.
Sadr's militia has been battling US-led occupying forces across south and central Iraq since Sunday.
Around 25,000 US troops are stationed in Kuwait, a key US ally, but their number can fluctuate with rotation of troops from Iraq. Kuwait also hosts other occupation forces.