The row heated up on Thursday when Erdoğan accused Iraqi Prime Minister Nuri al-Maliki of acting "self-centred" and inciting tensions between the country's Shi'ites, Sunnis and Kurds amid a constitutional crisis in Baghdad.
Maliki in turn branded Turkey a "hostile state" and said Erdoğan's remarks "represent another return to flagrant interference in Iraqi internal affairs," according to a statement on his website on Friday.
"We don't differentiate between Sunnis or Shi'ites. Arab, Kurd or Turkmen, they are all our brothers," Erdoğan told reporters in comments reported by the NTV news channel.
"If we respond to Mr. Maliki, we give him the opportunity to show off there. There is no need to allow him to gain prestige."
Turkey, which is majority Sunni, has been seen as a key ally and even a role model for Iraq, because of its secular constitution and close relations with the West, including membership in NATO.
Iraq is Turkey's second largest trading partner after Germany, with trade reaching $12 billion last year, more than half of which was with the semi-autonomous Kurdistan region.
Baghdad has occasionally accused Ankara of meddling in its affairs since the 2003 U.S.-led invasion. Saudi Arabia, Iran and Syria have also been accused of destabilising their neighbour.
The bitter exchange between Maliki and Erdoğan came after the Turkish leader met Masoud Barzani, president of the Kurdish region, who has cultivated close relations with Turkey's government.
Erdoğan also met Iraq's Sunni vice president, Tareq al-Hashemi, who fled Iraq in December after a warrant for his arrest was issued, sparking the current political crisis in Baghdad. Hashemi is wanted on charges he ran death squads.
Turkey's Foreign Ministry weighed in on the dispute and issued a statement that said Turkey has no intention of interfering in Iraq or any other neighbour's internal affairs.
"The foundation of the political crisis in which Iraq finds itself is that Iraqi politicians seek to consolidate power and exclude others, rather than (follow) politics that are based on democratic and universal principles," it said in a statement.
"It is a fact that behind the misperceptions that led to the accusations against Turkey by Prime Minister Maliki, who instigated the crisis in Iraq, this wrong understanding of politics can be found," it said.
As long as they present no obstacles, Turkey seeks friendly relations with its neighbours, the statement also said. Erdoğan previously has warned that Turkey would not remain silent if a sectarian conflict erupted in Iraq. He is also a vocal critic of erstwhile ally Syrian President Bashar al-Assad's crackdown against a largely Sunni uprising.
Turkey is worried that the violence in Syria and growing tensions in Iraq could lead to a wider conflict between Shi'ite and Sunni Muslims in the region. Relations with Iran have also soured over Turkey's opposition toward Tehran's ally Assad.