Troops, tanks and helicopters have surrounded the southern Iraqi city for days in an offensive against Shia fighters led by Muqtada al-Sadr, with the local police chief threatening to crush all resistance by force.
But in a lengthy interview with PBS's The NewsHour with Jim Lehrer programme on Tuesday, Rumsfeld appeared to acknowledge intensifying protests by Shia communities throughout the Middle East.
"It's unlikely that the US forces would be the ones that would deal with the holy places," Rumsfeld said. "That's just not something that we are likely to do."
He said he believed soldiers from Iraq's fledgling national army "would be the ones that would deal with that because it's such a significant thing to the religion".
Thousands of Iraqis have protested against a heavy-handed assault on one of the most sacred sites of Shia Islam, with al-Mahdi Army fighters vowing to spread resistance throughout the Iraqi south.
Najaf is revered by Shia all around the world because it is the site of the Imam Ali mosque, the presumed burial place of Imam Ali ibn Abi Talib, the fourth caliph and the son-in-law of the Prophet Muhammad.