By Saif Hameed and Aref Mohammed

BAGHDAD/BASRA, Iraq (Reuters) - Iraq's powerful Shi'ite cleric Moqtada al-Sadr asked his followers to stop attacking offices of Iranian-backed Shi'ite political parties that he accuses of corruption, after authorities said they could resort to force to restore order.

Sadr's followers on Thursday and Friday stormed or attempted to storm offices of the Dawa party, the Islamic Supreme Council of Iraq (ISCI) and the Badr Organization in five southern cities, according to the provincial authorities of Basra, Amara, Kut, Nassiriya and Najaf.

The provincial authorities did not report any casualties during the incidents.

Authorities "will stand up with force and firmness to deter the violators," Prime Minister Haider al-Abadi, who belongs to Dawa, said in a statement on Friday evening.

"Pressure on the corrupt political parties has to be done in a peaceful manner," Sadr said in statement addressed to his followers, posted on his website Friday evening.

Dawa has led most governments formed after the overthrow of Saddam Hussein, a Sunni, by a U.S.-led coalition in 2003, with major participation from ISCI and Badr.

While Sadr also had ministers in post-Saddam cabinets, including three in the current Abadi government, he has led protests over the last four months demanding Abadi replace politically affiliated ministers with independent technocrats.

The cleric also promised earlier this year to punish those suspected of abusing their official positions to get rich.

Iraq, a major OPEC exporter which sits on one of the world's largest oil reserves, ranks 161 out of 168 on Transparency International's Corruption Index.

The dispute within Iraq's majority Shi'ite community began turning violent when Sadrist protesters stormed Baghdad's heavily fortified government district, known as the Green Zone, for a second time, on May 20. Four demonstrators were killed.

Sadr's followers have been staging protests demanding anti-corruption reforms since February. His rivals see in the demonstrations an attempt by the cleric to dictate his views to the rest of the political class.

The Sadrists have not staged protests near the Green Zone since Abadi ordered an offensive on Falluja, the stronghold of Islamic State militants near Baghdad, on May 23. But they continued to demonstrate in other parts of the capital and in other provinces.

(Writing by Maher Chmaytelli; Editing by Dominic Evans)