0228 GMT December 11, 2018
According to Press TV, Lagarde said that the discussions focused on global developments and economic challenges facing Iran, as well as the key reform priorities needed to safeguard macroeconomic stability at this time.
The official website of Iran's presidency reported that Rouhani told Lagarde that Tehran is willing to deepen relations with financial institutions, especially the IMF, and benefit from the fund's advice.
Rouhani described US sanctions against Iran as "illegal and contrary to international laws and stressed the need for international financial institutions to support Tehran against this illegal US action", it said.
The Iranian president stressed the IMF's primary responsibility is to protect its members against infringements as well as banking and monetary sanctions.
"The IMF should demonstrate that it can play its part in the economic stability of a member, and I hope that it can take a positive step in this regard," Rouhani said, according to the website.
Iran is facing challenges for access to the global financial system under new sanctions imposed by the US which withdrew from an international nuclear deal with the Islamic Republic in May.
US banks are forbidden from doing business with Iran. Lenders based elsewhere also eschew dealing with the country because unilateral American rules prohibit transactions in dollars from being processed through the US financial system.
The International Monetary Fund along with the World Bank and the Financial Action Task Force (FATF) assesses countries' compliance with recommendations to combat money laundering and financing terrorism.
The inter-governmental organization FATF has given Iran until October to address nine action items or face blacklisting and counter-measures.
To fulfill FATF requirements, the Rouhani administration has proposed four bills to the Parliament for approval, two of which are still undecided, including the Palermo Convention.