They also accused neighbouring Shia-dominated Iran of trying to fuel growing religious tensions in the country by reaching out to Moqtada al-Sadr, a powerful young cleric known for his virulent opposition to the US-led occupation.
The Shias "have taken over the al-Hamza mosque, our only one in Najaf, and the Hassan bin Ali mosque, our only one in Karbala," a spokesman for the Council of Ulema (religious scholars), Sheikh Abdel Salam al-Kubeissi, said.
"Emptying Najaf and Karbala of Sunni presence is a grave phenomenon akin to sectarian cleansing and (conducive to) the Balkanisation of Iraq," he said.
He also accused Shias of taking control of 16 other Sunni mosques across the country, including a dozen in Baghdad. The claim could not be immediately verified.
But Kubeissi said the Ulema Council had called for calm among its followers in the face of "provocations from some Shias."
"We are being quiet, not because we are cowards, but because in the current situation it is necessary that we remain calm."
But in a broadside at Iran, the Ulema Council also accused the supreme leader of the neighbouring Islamic Republic, Ali Khamenei, of pressuring Shia cleric Moqtadaal-Sadr to cut ties with the Sunnis.
"Emptying Najaf and Karbala of Sunni presence is a grave phenomenon akin to sectarian cleansing and (conducive to) the Balkanisation of Iraq"
Sheikh Abdel Salam al-Kubeissi, spokesman, Council of Ulema in Iraq
"We had a minimum of coordination with Moqtada al-Sadr but he changed about 40 days ago after a meeting with Khamenei in Iran," Kubeissi said.
"Iran has entered the Iraqi scene. It looks badly on meetings between Shias and Sunnis, a fraternisation between (Sunni) mosques and the Husseiniyeh," or Shia holy places, he said.
Al-Sadr has risen to prominence in the power vacuum of post-Saddam Iraq, tapping the followers of his father, a revered grand Ayat Allah who died in 1999.
Explaining the formation of the Ulema Council, Kubeissi said it was created on 14 April, five days after the fall of Saddam Hussein. He said it grouped all the country's Sunni ulema.
His comments came as hundreds of thousands of Shias thronged Najaf, a pilgrim city 180 km south of Baghdad, to bury Ayat Allah Muhammad Baqer al-Hakim, a revered cleric whose death in a car bombing outside a shrine there has thrown the country into turmoil.
Iraq's Shias make up 53% of the 25-million population.