The director of the al-Sadr office in Nasiriya, Aws al-Khafaji, told Aljazeera the damage occurred during clashes between the occupation forces and the al-Mahdi Army on Sunday night.
Supporters of al-Sadr said US aircraft had fired a rocket into the outer western wall of the mosque compound, news agency AFP reported.
The US military denied that the shrine had been targeted.
There was a dent in the wall measuring about one square metre and 30 centimetres deep, with rubble and spent parts of a rocket littered on the marble floor, an AFP correspondent said.
"It was around 11pm (1900 GMT) to 11.30 pm. Two rockets were fired from an American Apache. One hit the western wall of the shrine and the other a nearby hotel," said al-Sadr aide Shaikh Ali Husayn Ali.
Shia fighters have an advantage
on the narrow streets of old city
The hotel is a known resting place for commanders in the al-Mahdi Army.
Balance of power
Iraqi journalist Husayn al-Haidari told Aljazeera that "clashes are continuing and street battles are raging close to the Imam Ali shrine, about 400 metres from it".
On whether the al-Mahdi Army was still as strong as they were before the battles started, or had the US forces gained the upper hand, al-Haidari said the US troops were getting regular reinforcements around the old city area of Najaf.
"The US forces seem to have more power than the al-Mahdi Army, which has only light weapons such as mortars and automatic machine-guns," said al-Haidari.
On whether the geographic characteristics of the area gave al-Sadr's fighters the edge, al-Haidari said the entire area of the old city was about one square kilometre. "The streets are narrow - about three metres wide and not straight," he said.
"This gives the fighters some leverage in streetfighting and to ambush advancing US troops," the journalist said.
US forces around the shrine are
getting 'regular reinforcements'
In the fighting on Sunday night, one person was killed and three wounded, said a doctor at a clinic in the shrine, with another four patients brought in on Monday morning.
At about 2am on Monday, a US AC-130 warplane attacked al-Mahdi positions.
Later on Monday morning, US troops and Shia fighters fought fierce battles in Najaf with multiple explosions and gunfire echoing around the Imam Ali shrine.
At least 10 explosions, some sounding like artillery shells, rocked the area near the shrine.
Shrapnel landed in the courtyard of the gold-domed mosque, near the already-damaged outer walls.
US tanks were not visible in the neighbourhood of the shrine, where previously they were parked within 200 metres of the compound.
In the shrine's courtyard, dozens of fighters and civilians turned towards the shrine itself to chant repeatedly "Muqtada we are with you", "Imam Ali we are with you."
Al-Sadr aide al-Khafaji said al-Mahdi Army fighters were still controlling the old city area near the shrine in Najaf.
The keys had not yet been delivered to Shia cleric Ayat Allah Ali al-Sistani as some related issues were still to be sorted out, al-Khafaji said.
"Sons of the city are
the only ones who
should protect the shrine. Al-Mahdi forces are the sons of the city and are ready to protect the shrine"
Al-Sadr aide Aws al-Khafaji
Even if the keys were delivered to al-Sistani, the al-Mahdi Army would continue to protect the Imam Ali shrine "as it can never be protected by the Americans or even the Iraqi police forces who have stained their hands with the blood of Shia Muslim Iraqis", al-Khafaji said.
"Sons of the city are the only ones who should protect the shrine," he said. "Al-Mahdi forces are the sons of the city and are ready to protect the shrine."
"Al-Mahdi forces who will protect the shrine, should necessarily not be armed," al-Khafaji added.
Al-Sadr spokesman in Najaf Shaikh Ahmad al-Shaibani also told Aljazeera's correspondent the al-Mahdi Army would continue protecting the shrine even if al-Sadr handed over its keys to al-Sistani.
The fighting in Najaf has triggered protests in seven other southern and central cities, including Baghdad.
Serious damage to the mosque precincts could enrage millions of Shia Muslims and fuel hostility to the US presence in Iraq.