The lawmakers gave the greenlight while discussing the budget bill for the next Iranian calendar year (starting March 21).
Russia had agreed to provide a $5 billion loan to Iran for joint infrastructure projects in October 2015, when Russian Energy Minister Alexander Novak travelled to Tehran.
Out of the $5 billion, the Iranian side has so far received $2 billion and now can get the remaining $3 billion.
The removal of the nuclear sanctions in 2016 triggered a race among international companies to tap into Iran’s lucrative market.
However, the withdrawal of the US from the nuclear accord last year has scared away international firms.
Russia, a party to the nuclear accord, has frequently voiced its opposition to the US withdrawal from the pact.