The two leaders discussed the protests across Iran that have been ongoing since December 28, the source said.
Erdogan stressed on the significance of maintaining peace and stability in Iran. He also welcomed Rouhani's remarks on urging the public to not violate their country's laws while exercising their right to peaceful protests.
Rouhani told Erdogan he hoped the protests in Iran would end within a few days, the source, who spoke on condition of anonymity due to restrictions on talking to the media, said.
Thousands of Iranians took to the streets Thursday in the northeastern cities of Mashhad and Kashmar to protest against rising commodity prices and perceived government mismanagement, according to local media reports.
The anti-regime protests were followed by pro-government protests on Saturday and Wednesday. At least 23 people, including a police officer, have been killed and more than 1,000 reportedly detained since the demonstrations began.