The U.S. military said gunmen killed three of its soldiers in Baghdad on Monday, a day after seven were killed across Iraq.
Senior Sadr aide Hassan Zargani said Sadr would seek rulings from Grand Ayatollah Ali al-Sistani, Iraq's most senior Shiite cleric, and senior Shiite clergy based in Iran, on whether to dissolve the Mahdi Army, and would obey their orders.
"If they order the Mahdi Army to disband, Moqtada al-Sadr and the Sadr movement will obey the orders of the religious leaders," Zargani told Reuters from neighboring Iran, where U.S. officials say Sadr has spent most of the past year.
However, Sadr's spokesman in the holy Shiite city of Najaf, Salah al-Ubaidi, said the idea of disbanding the militia was not new and there was no plan to seek a ruling from top clerics.
"Sadr is willing to dissolve the Mahdi Army if the higher religious authorities order him to do so. (But) this is an old idea and didn't come in response to Maliki's orders," he said.
Sadr had consulted religious leaders a year ago and they had rejected the idea of dissolving the militia, Ubaidi added.
Sistani, 77, who almost never leaves his house in Najaf, has intervened in Iraqi politics only a handful of times but on each occasion his rulings have been decisive.
Iraqi government spokesman Ali al-Dabbagh said he could not comment on the matter. Sistani's spokesman, Hamed al-Khafaf, declined to comment.
The announcement of the offer comes at a pivotal time, two days before Sadr has called a million followers onto the streets for anti-American demonstrations and one day before the top U.S. officials in Iraq are due to brief Congress on progress.
Maliki ordered a crackdown on the militia two weeks ago in the southern city of Basra, provoking clashes throughout Baghdad and the Shiite south that led to the country's worst fighting since at least the first half of 2007.
That fighting ebbed a week ago when Sadr ordered the militia off the streets, but picked up again on Sunday with clashes around the Mahdi Army stronghold of Sadr City, a Baghdad slum.
Fighting continued in Baghdad on Monday, although not with the same intensity as Sunday's clashes.
Meanwhile Iran announced on Monday that it had received a "request" from its arch-foe the United States to hold a fourth round of talks on security in Iraq.
"We have received a new request from U.S. officials through a formal note for holding talks on Iraq and we are looking into the issue,"
Foreign ministry spokesman Mohammad Ali Hosseini told reporters that the note had been received through the Swiss embassy in Tehran, which looks after U.S interests in the Islamic republic in the absence of a U.S. mission.
No talks between the two sides have been held so far this year amid continued tension over Iran's role in its conflict-torn neighbor.
An Iranian delegation traveled to Baghdad in March in expectation of a new round of talks that never took place. Iran said the United States cancelled the talks at the last minute, but U.S. officials said the date was never set.
Iran and the United States held three rounds of talks about Iraq last year despite mounting tensions over Tehran's nuclear programmed. The two foes have had no diplomatic relations since 1980.
U.S. ambassador to Iraq Ryan Crocker and his Iranian counterpart Hassan Kazemi Qomi held face-to-face talks in May and July last year, the highest level public contacts between the two sides for 27 years.
Officials from both countries also met at experts' level last August, but there has been no meeting since.
The United States accuses Iran of meddling in Iraq by helping to train Shiite militias and shipping in amour-piercing bombs for attacks against U.S. troops. Iran vehemently denies the charges.