"A US patrol violated the truce by approaching Najaf from the Valley of Peace area at about 8:30 am (04:30 GMT) this morning," Shaikh Mushtaq al-Khufaji told reporters on Sunday.
"Members of the Mahdi Army confronted it with rocket-propelled grenades and gunfire, forcing it to retreat."
The clashes, which started around 9:00 am and lasted about one hour, erupted around the northern extremities of the city's vast cemetery, known as the Valley of Peace.
"Medics at the city's hospital said three people were wounded," reported Aljazeera correspondent adding that al-Sadr's office accused the US forces of starting the fighting.
The area is less than two kilometres from the city centre and has been the scene of fierce clashes in recent weeks between US troops and al-Sadr's Mahdi Army militia.
Residents rushed for shelter and Najaf's streets looked deserted again after normal life had slowly started to return to the city following the announcement of the truce on Wednesday.
US tanks and armoured vehicles were also seen around the nearby 1920 Revolution Square, witnesses said.
"I saw US tanks and armoured vehicles moving from the police headquarters towards the square," said Mahdi Abd al-Razzak.
Al-Sadr is wanted in connection
with the murder of a Shia leader
Fighting resumed in the mid-afternoon when mortar rounds and rocket-propelled grenades rocked the cemetery area as US tanks made another approach.
Khufaji said the Mahdi Army "is committed to the truce", which was offered by al-Sadr and cautiously welcomed by the US-led occupation.
But he said it was "ready to respond to any US violations". "We consider the running of US patrols anywhere outside the stretch connecting the (US) base and the governor's office a violation of the truce," he said.
US troops have been stationed at an occupation base on the eastern fringes of Najaf for more than a month and have also deployed at the provincial governor's office since recapturing it from al-Sadr's militia.
US commanders have said they will abide by the truce but troops will continue to run patrols in Najaf and will defend themselves if attacked.
Three people were wounded
in the latest Najaf clashes
The ceasefire is intended to allow for negotiations on the fate of the Mahdi Army and legal proceedings against al-Sadr, who is wanted in connection with the murder of a rival leader last year.
Also on Sunday, tens of Iraqis took to the streets of Najaf protesting against the assassination attempt of Shaikh Sadr al-Din al-Qabanchi of the Supreme Council for the Islamic Revolution in Iraq (SCIRI), reported Aljazeera correspondent.