Militia fighters say they could resume violence if provoked by US troops.
No specific time-frame for the investigation was given, but the statement said it would be concluded “as soon as possible”.
Al-Sadr, who has denied that the Mahdi Army provoked the confrontation, announced a surprise six-month suspension of the militia’s activities on Wednesday in an apparent bid to deflect criticism.
Al-Maliki’s office said the al-Sadr movement was “considered one of basic political blocs in Iraq and will remain an active and a real partner in the political process”.
A statement from al-Sadr called that comment “just ink on a pen”.
On Sunday, al-Sadr threatened to take matters into his own hands if the government didn’t open an investigation.
In Najaf, Sheikh Salah al-Obeidi, a spokesman for al-Sadr, said: “After the procrastination we had seen in the past two days, we warn the Iraqi government and the executive authorities in Karbala if they don’t open a fair, neutral and quick investigation, the Sadr office will be obliged to take unspecified measures.
“We are trying our best to save the blood of Muslims to stem the strife.”
A statement from al-Sadr’s office said that more than 200 of his followers had been detained by Iraqi security forces in the past three days in Karbala.
Iraqi government has said 72 people had been detained, and that al-Sadr’s followers were not being targeted.
Jawad al-Hasnawi, an al-Sadrist member of Karbala’s provincial council, said al-Maliki had promised to stop detaining people in connection with the incident but “despite the promises … detentions are still going on”.
He said: “They have taken us back to the era of the former dictatorship.”
Baghdad car bomb
Meanwhile, Iraq suffered another day of violence. A car bomb exploded on Eddin Square in northern Baghdad, killing nine people and injuring 15 others, police said on Sunday.
US soldiers killed “eight extremists and arrested for others” in a series of raids in Baghdad, the US military said. Troops also freed nine Iraqi hostages during the operation, the command said.
A suicide driver detonated his truck at an Iraqi army checkpoint near Taji, just north of Baghdad, killing one civilian and six other people, three of them soldiers, Iraqi police said.
Also on Sunday, Rear Admiral Mark Fox, the US military spokesman, confirmed that US forces arrested six people in a raid on Thursday at the government newspaper Al-Sabah in Baghdad.