Conte made the remarks during an hour-long phone call with Erdogan which was "extremely tense at times," according to sources in Conte's office.
Conte reiterated Italy's request that the Turkey stop its military incursion in the border area with Syria, which has created new humanitarian crisis. At least 160,000 civil have fled their homes and there are security fear over thousands of Islamic State jihadists abandoned in Kurdish jails.
A statement issued later by the Italian Prime Minister's Office said Conted told Erdogan that Nato member Turkey should play its "strategic" geopolitical role "responsibly" and halt its military action in Syria.
"Conte repeatedly urged Erdogan to responsibly play its strategic geopolitical role and that of Nato ally and act in the collective interest of the entire region's stability," it said.
Italy's public and politic back the government's view that Turkey must stop its week-old military offensive in northeast Syria, said the statement.
Turkey's "unilateral initiative" is having "negative and counter-productive" effects and is causing "a humanitarian crisis, suffering and displacement," it said.
"Conte invited Erdogan to withdraw Turkish troops from the area to prevent the humanitarian crisis getting worse as well as jeopardising the fight against the Islamic State and United Nations efforts to reach a political solution (to the Syrian conflict)," the statement said.
Protecting Syria's civil and ending the country's eight-year civil war are "inalienable priorities for Italy and the whole of the international community," Conte told Erdogan, according to the statement.
Turkey's Operation Peace Spring offensive in northeast Syria began on 9 October after United States President Donald Trump said that US forces would withdraw from the region.
/AKI
( With inputs from IANS )